It is not legal
So, your comments have encouraged me to get off my ass and do some detective work. The last 5 students to graduate had their insurance cut off the day they took their paperwork in. However, in the insurance information book, it claims that we will have our insurance until August 14th, even if we graduate before that.
The student insurance office has confirmed the information booklet. I did not get a straight answer on the COBRA stuff.
Now I must go snoop around the University administration offices since the insurance company is claiming it's innocence.