This answer is for educational discussion and not for legal advice.
I am not certain that your parking lot is considered private for purposes of handicapped parking. For example, I had an accident in the parking lot of a Kroger. It was my fault. The police could not ticket me, because it was private property. But, if I had parked in the handicapped spot, I could be ticketed under the law regarding disability. When a property is open to the public, which I assume your fraternity parking lot is - you have parties, & there are a large number of people coming & going - such as at an apartment complex - then it is probably considered quasi public. (Comparing it to an apartment complex lot - you know that there are handicapped spots there, and of course that property is private - most the times even having gates that prohibit entry unless you have a code - but they can still ticket you for parking in the handicapped spot.
Why don't you find one of your alumni who is an attorney, ask him to check the parking rules, and then follow his advice? Otherwise, you can appear in court to fight it, but I think that not only will you lose, but you will look like a bad person for not being considerate.
I believe that in the future, if the spot is marked handicapped as required by law, then only persons with handicapped tags can park there, and you might just consider this a lesson for the entire group.
Once again, I do not know this for certain, but when you think about it logically, it makes sense. (I know, for example, that some older buildings were grandfathered to the handicap access laws UNTIL they made some renovations. If they made ANY renovations, they had to include making handicap accessible parking to the building & handicap access in the building - even though the building was private property.)