Who knows if it's a scam, wouldn't worry yourself about it.

We thought we had a good possibility, but I believe it's a scam.

There is nothing in it for you and if she is running a scam she will be in the property for a lot longer than a few months.

It may be possible, I am not say n that it is, but possibly this woman does this on a continual basis - a scam artist?

If they do not have a good one, I can GUARANTEE you this is a scam. 

I am really stern about stuff like this because I've read sooo many articles in the news about how some novice landlord got scammed by a professional tenant because she didn't do a background check, didn't get rent upfront, didn't have a signed lease, etc.

Candidate selection is extremely important otherwise you end up with the old scam of churning candidates destined to fail.

Otherwise every person could just claim every animal is a "companion", but I'm sure they are not.There are problems with online "doctors" who claim to give prescriptions or recommendations for companion animals to whoever pays for one, however, these are mostly scams, and I don't think landlords actually are required to accept their fake "prescriptions" if they don't actually have a proven doctor/patient relationship.

Or was she scammed?  

There are people out there who make a living out of screwing over unsuspecting and inexperienced landlords by working the system.