Wow, when I first read through this, I started chuckling a bit with the whole deal involving the "pit bull assistance dog", yet another section 8 tenant who when given an inch always takes not just a yard, but several yards, etc !!! I don't know if I should laugh at what sounds like more absurdity or pull my hair out pondering the future of our awesome country, which so often seems to be devolving into a sad paradise for people who know how to game the system!
Yet, taking a step back from all of that, I think you really need to take this matter seriously and to proceed with much caution and forethought! First off, no matter how ridiculous the whole idea of having a pit bull as an assistance dog to help with depression may seem at first, the truth is that in SOME cases, depression and/or other mental issues can certainly cause people severe disabilities that are just as debilitating as any physical condition. No, its not anything obvious like someone who's confined to a wheelchair, but it can still really ruin people's lives and it can't be proven or disproved with an X ray or a cat scan that can show whether or not a spinal injury for instance, is really there or not. So, assuming that you're not a psychiatrist, I'd avoid dismissing the validity of this doctor's letter on your own. Also, while the prior malpractice claims may tell us that this doctor is a quack, it also could be a red herring, too!
I'm wondering if you should just go to your insurance company on this or not? I'm not 100% sure, but I think that even if your ins company bans pit bulls (which it seems like pretty much every ins co. does these days) I think there is a law exempting service dogs, much like how service dogs are exempted from being barred from going in to stores, restaurants, etc. So, I would think that the insurance company would likely want to have their attorneys investigate whether or not this particular pit bull is really a legitimate service dog or ESA or whatever they want to call it. Obviously, if you want to keep this quiet from your insurance company, you could just hire your own legal counsel, but we all know that will likely cost a bundle! I guess you have to weigh out whether or not you want your ins co to know about this, I personally would lean towards getting them involved.
My final thought also involves the tenant's threat of getting legal aid involved. This goes back to handling the whole issue of the mental illness claim and all of that. I'd tread carefully there as well because you also certainly do not want some bleeding heart legal aid attorney getting the impression that you are some "evil landlord" that evicts tenants with depression and/or mental illness because you don't like ESA dogs. You just might light a big fire under that attorney and cause him/her to come after you as hard as they can to make an example out of someone they think is abusing the mentally ill! It may sound far fetched, but its not out of the realm of possibility! So, what started out as some section 8 tenant using a bogus depression claim to find a back door way to keep a pit bull could turn into something totally different, there certainly are activist lawyers out there always looking for a cause!
EDIT: After posting that original comment, I saw this thread which I'd certainly recommend you read:
http://www.biggerpockets.com/forums/52/topics/104090-federal-housing-laws-service-and-support-dogs-landlords-rights
It spells out pretty clearly some of what I'd assumed, that service dogs are exempted from dog bans. Having been in the restaurant biz for a while, I know that the ADA (Americans with Disabilities Act) is nothing to take lightly or mess around with, they can really hang you! Also, as I touched on, even if you think or are even totally sure that this pit bull service dog is just a sham, being backed up with a letter from a sham doctor (which may well be true, I'm not denying its possible!) don't waste your time fighting that case yourself, you'll need a comparable expert to disprove that doctor's letter, even if its plainly obvious to be total crap!