If she were a human I'd say go ahead with the antibiotics because they probably can't do any harm (maybe more diarrhea=/). Is there any way to contact the owners of the other puppies and see if they are having issues?

I think I'd see another vet. Antibiotics and a new vet visit.

(Sounds like she's acting like a normal puppy--congratulations!)

Antibiotics can indeed do harm especially in young animals. Certain classes of antibiotics can cause severe tendon problems, tooth problems, bone problems, and kidney failure just to name a few. Not to mention adding to the problem of antibiotic resistant infections. Others are safer for puppies but just because a vet prescribed an antibiotic doesn't mean it's safe for your pet. Especially since they didn't even do a full physical exam.

Just because a parvo test is negative does mean the puppy doesn't have parvo, although a low platelet count without a low white blood cell count is very unusual. There are a few ways this could happen but a negative test does not necessarily rule out parvo infection.

Was the puppy dewormed? That is a very common cause of vomiting, diarrhea, and lethargy in puppies, especially strays. I'd deworm regardless of fecal results for at least roundworms, hookworms, and whipworms because again, a negative test does not necessarily rule out infection.

As far as the platelet count, I'd run the test a second time on a new sample. Could be a simple matter of the blood clotting or platelets clumping, which would screw up the results both by the machine at the outside lab and manually. With a platelet count of 13,000 you'd expect some clinical signs...