Joe:
This is Federal Law from HUD. While it is probably well-intended, it is horrible regulation.
We've seen a ton of this. It seems to me that almost every time you get an ESA request for a restricted breed, it is probably someone just trying to get around breed restrictions and having to pay pet rent. About 60% of our ESA requests are pitbulls. (I just don't see how a pitbull could offer more emotional support than a poodle or spaniel.)
I'd encourage you to google HUD guidelines for Emotional Support Animals. They have a ~15 page PDF that describes the rules. READ IT AND KNOW IT.
We have a fairly simple process at all our properties. We require documentation that the owner requires an ESA. The evidence they provide must be from a medical professional licensed in our state and the letter must indicate the medical professional has had more than a one-time tele-health "diagnosis". If the evidence does not pass all of those hurdles, we have a form letter that they have not provided sufficient proof of an ESA.
Do not explain. If you choose to explain exactly what proof you need, you will soon get it. There are plenty of people that for $100 will use their medical license and type up a letter that their patient needs an ESA.
Also, if the ESA exhibits any aggressive behavior it can be removed from the property IMMEDIATELY. We recently had an ESA Great Dane (with all the proper ESA documentation) that bit another resident. Dog was gone as fast as we could make it happen.