Oh! Noes! is right- you might have yourself a problem here, as sanding and refinishing will likely be required. Bleaching or oxalic acid crystals can help remove the dark stain, but you still have to worry about matching the finish when you restain.
Depending on how much of a deposit you stand to lose it may be worth your while to hire a floor guy.

Always put plants into a waterproof outer pot and elevate with pot feet. And even than I'd rather see then up on some sort of low stand.

One of our rental properties has original oak hardwood from the 1920's. I have a couple suggestions.

You could test some Restore-A-Finish. (I've not used that on floors, but have used it with great success on antique furniture that needed a little TLC but not a full strip-refinish.) Many hardware stores carry it, Sears Hardware has the best selection of tints. Since I use that on furniture I finish off with their suggested Howard's beeswax for shine. Do not put beeswax on the flooring, it will be slick as ice!

Here's a vintage solid cherry hutch I got on eBay that I used RAF on:
Seller's ebay photo

After RAF and beeswax (I used Mahogany and just a bit of the Cherry tint)

I've also brought the rental hardwood floors back to life with a product I found at Home Depot. It's called Rejuvenate. Thought it looked gimmicky, but didn't want to strip/refinish all the floors in the rental house, for the $$ it would cost and the beating they take it wouldn't last long. (Even flooring guy that gave me a refinish estimate suggested we hold off till it's no longer a rental. ;-) Overall the floor was vile filthy from prior tenant, with a couple bad spots where finish was worn. In one of the bedrooms were a couple black circles like burns. Flooring guy said it was probably cat urine. (No pets allowed, so someone snuck it in.) Anyway, Rejuvenate got about 80% of the black mark out. It did wonders for the appearance overall and held up a good couple year before I did again between tenants. Didn't hurt the flooring, either (it was 4 years ago I first put it on).

If you use that route you'll need to do the entire floor so it will match. And top priority is to clean it really well first. Do not use vegetable based products like Murphy's, it will gum up the floor's finish. I forget what I cleaned the floor with (sorry, it was so long ago), but be sure it's a product that doesn't leave any residue. I didn't just mop clean it, I used a little more water than normal but almost immediately sucked up the water with DH's giant shopvac (to get gunk out of grooves of floor). Then cleaned again a couple times with my Hoover Floor Mate to suck up any water/moisture. Doubt you want to go to that extreme, but my point is that floor was just gross and I wanted zero dirt left on it before apply Rejuvenate, because it acts like a sealer (just not permanent like varnish). Rejuvente goes on like a liquid wax, with a lint free cloth or mop. So if you clean the usual route maybe do it by hand with rags and clean till there is no dirt left on the rags. One bottle of the Rejuvenate ($17) was enough to do about 800 sq feet for me (liv room and 2 bedrooms).

Here are before/after with Rejuvenate, old solid oak floors:
Older camera so resolution is not great, but where reflection comes in through front door you can see how gunky dirty and dull the floor was (and makes me shudder all over again).

After

Actually, the ultimate solution might be to put the color back in the floor with the Restore A Finish, and then go over the whole floor with the Rejuvenate. Probably talking $20 and an hour or two of your time. ;-)