Check your city/state laws on it; they have narrowed the rules for the ADA requirements. Here's Seattle, Washington's, for example:

http://www.seattle.gov/civilrights/d...ce_animals.pdf

Everyone loves their pet so I'm sure they are rather strict on how a service/support animal is defined; not any way to enforce what you say/your piece of paper against them either, places don't usually tell you why you do not qualify for an apartment, just that you did not get it. You'd have to prove it was because of the rabbit, and go through a long legal thing, etc.