A roof covered in snow can't be properly inspected.
Hard-to-locate leaks are frequently due to problems with flashing around chimneys, vent pipes, etc, especially when a second layer of shingles are installed without special attention to those locations.
Tarps have a short lifespan as roofing. The common ones deteriorate from sunlight and tear easily.

It sounds like you are making the best attempts possible to get it resolved. The number of claims filed following sandy pretty much assures temporary help to get claims processed. Full time adjusters are not profecient in all types damage,temps and part timers even more so. The adjuster returnibg with a "supervisor" probibly means "better quilified" adjuster simply because first one isn't totaly confident he is correct. Chances are the roofer will charge to be there so I would pay him. Just make certain the roofer knows his business and is confident in his conclusions. I agree that locating a leak where there are 2 layers is difficult if not impossible.
If there was never ceiling stains before the storm I would say one or more of these is true.
A. The roof was damaged B. Insulation was disturbed and covered soffit vents C. Water was driven under shingles and is unlikly to leak again.
In any event,the attic has enough vents or it doesn't and can be asertained by simple measurments.

See if you can delay the inspection until after the spring thaw.

Hire a public adjustor. That will break through much of the run-around.

Meanwhile, inspect in the attic yourself while it's raining and on a bright, sunny day (even with the snow and if it's below freezing). If you see water or any dripping, you have a roof leak. On a separate note, look at the roofing nails inside. If they are rusty, you may also have condensation and ventilation issues. Still, you could have a roof leak, as well. Also check near all the roof penetrations on those days (plumbing vents, etc). Also check every joint on your plumbing vents. Maybe there's one that wasn't glued properly, esp. one of the horizontal ones. (hint: look directly over your ceiling damage). I've seen that a couple times. When it rains, water goes down the vent and leaks out a bad joint, etc.

Good luck.

Thank you all so much for responding. I understand better what must be done, and which concerns are legitimate. The man who performed emergency services will come out for the re-assessment tomorrow. Hopefully that, along with some insights you've given me, will make me better prepared this time.

randy427, unfortunately, the first floor roof has been tarped for over a year now. I'm hoping it will be replaced soon. The adjuster wants to come tomorrow morning and the roof will still be covered in snow and likely ice; I recommended they wait till the Friday thaw, but they're coming tomorrow anyway. They did mention in the first assessment that there was a collar around a vent that appeared to be loose. Maybe that's the source.

klem1, the adjuster is returning with his supervisor because I wrote a letter to the vice president of claims asking that he send someone else out. The men they sent were so unprofessional, and after that comment about the buckets and other nonsense, it seemed a prudent request. The attic doesn't have enough vents by today's standards.

snoonyb, I tried. no-go.

homebound, a public adjuster would be the next step. I hope it's not necessary. The man who did the emergency service and will do the roof repair promised he'd come. You put it so succinctly - I probably have venting issues; that doesn't mean I don't also have a leak. I'll try to get up there tomorrow morning and see if I can find it myself.

Again, thank you all for weighing in. I appreciate you taking the time to share your knowledge.

EAM44:

I lived in a condo that had a "roof leak". Turned out the run of the furnace flue was so long inside the attic, it allowed the gas to condense and drip creating the "leak". Things are not always what they seem to be.

Makes perfect sense to me.

If the roof is covered with snow and ice and is not leaking,.............It must be fixed.

Who'd a thought.

Well, hard to know how it went. They came, they saw, they left ten minutes later because they couldn't get up on the roof. Didn't bother going into the attic. At least they talked with the roof guy and they seemed to listen to him.

trebuchet - noted. thanks.

snoonyb - yeah, well what can you do. There was a bit of a thaw today but too much snow still on the roof for them to get on it. Tomorrow the roof will be clear. Whatever. The spots are bigger. I had trouble with my ladder so I'm going to try to look in the attic myself tomorrow.

Thanks guys.

where the water stains show on the ceiling aren't
always where the roof leaks.
for instance if the ridge vent leaks the stain is
often lower down on the ceiling as water
drains down.
I've seen chimney flashing leak & the water stain
on the ceiling was several feet lower than where
chimney was located.

I'm not in a climate where we have to worry about
snow, but a thermal scan of the roof would show
moisture intrusion into the attic.

rather than being sold a bandaid patch, I'd
invest in thermal scan (Infra red camera) of
roof before settling for something that isn't
actually fixing the issue.

I'd second inspecting all venting, flashing &
vent caps. water dripping from nails can also
come from conditioned space air leakage into
attic, as well as unvented bath fans.

if at all possible hold off until spring to determine
what needs to be done. they wouldn't be
replacing roof in the snow anyway would they??

its a tough spot to be in...we often have hurricane
damage that requires more than insurance pays for.
the insurance company just wants to write you a check
& move on. they are not worried about addressing the
issues as they are about just settling.

get opinions/estimates from several roofers.
but only roofers who have been in business IN YOUR
AREA for several years. La. is still addressing lawsuits
from roofers from other states who came here to rip off
homeowners. most of these companies take your money
do a crap job & then are unavailable when issues re-occur.
don't hire fly by night out of state roofers!

best of luck.

Thanks energy. I'll look into a thermal scan. My contractor is local. I didn't realize there were issues with that, but thanks for bringing it to my attention.

I'm still waiting to hear back from the insurance company. I'll let you know how it goes.

Assuming that your roof is water stained, its a protected wager you have either a top hole or a buildup issue. It's imperative to resolve what sort of stain you have before you repair your roof.

Luckily, these stains are not difficult to recognize. The buildup stain is typically found on a roof board close to an outside divider, regularly in a corner. Rather than one substantial stain, you'll see a few littler loops of stains. These stains fluctuate fit as a fiddle, yet they have a tendency to have white focuses. Buildup stains seem regardless of the possibility that there has not been a rainstorm.

The drizzle break stain might be discovered anyplace on your roof: close to an outer surface divider, encompassing a roof apparatus, around a ventilation pipe or even in the middle of the roof. This stain has a tendency to be concentric rings that get dynamically lighter as they move outward. The middle stain is dull, on the grounds that it is the most senior stain. Each one "ring" incidentally, is a divide event. When you see bunches of rings encompassing the dim stain in the center, you know the top spill has been around for a long while.

Thanks epdm. My stains are sort of linear. I'll post an image if I can. They run both perpendicular and parallel to the ridge line. Since I had emergency service when the damage occurred I'm not sure whether they are getting worse or not, or whether the "fix" was temporary. Again the roofer and adjuster disagree...

I've seen ridge vents pull in water during hurricanes.
it may have been a one time (super storm whatsit)
issue.
hope so anyway!
it makes sense, if the water stains are at ridge vent.

keep us informed.

best of luck.

Hey guys. Just wanted to update you. The insurance company is replacing the roof. Which is to say, they are covering the depreciated cost of replacement. If you have any recommendation re:asphalt shingles, please let me know. I wanted to do a metal roof but the estimate I got was 25K, very over budget, more than twice the cost of asphalt.

Thanks again for your input. I'm pleased to be getting on with it!