Well, this hits home with me because my dog goes to PT twice a week and I have not taken special precautions other than holding her in the waiting room. I only do that because I worry about parvo, I didn't think about MRSA. I usually express her about 2 hours after PT, not right away, because she tends to drink the water in the treadmill and I like to give it a chance to process through her system, and she is always expressed 30 minutes before PT....
Here is an article on MRSA in animals, though you will probably never know where she got it.http://www.avma.org/animal_health/mrsa_faq.asp
You can get swim diapers at Sam's Dog Hut to protect her when she's scooting on the floor in PT.http://www.samsdoghut.com/catalog_g4.html?catId=358938
They do recommend expressing the bladder after the dog has been out in public, on a sidewalk or swimming in a creek. I do not know if that would have made any difference and in your position I would have assumed the water at PT was sanitized (the water in the treadmill is chlorinated, I don't know if that kills MRSA or not) and I would not have given much thought to the mats at the PT, if either of those had anything to do with it. I'm sure the staff or janitorial personnel walk through other parts of the hospital and then walk on the mats to some extent. Certainly other dogs are walked through the hospital and could track something in I suppose.
I know in humans they say a percentage of MRSA is community acquired, it's just out there in the community and you don't have to get it in a hospital, you can pick it up anywhere.
As far as the diapering, if she is soiling and getting it on her female area, it would probably be good to diaper her just to prevent regular infections. Dry stools would also be helpful. I kind of doubt she got MRSA from her stools, but that is a totally uninformed opinion, I'm not a vet.
I still don't know what to say, this is a shock. How long does she need antibiotics?