My opinion, which is worth less than 2 cents, is that Lady Gaga was going to steal the attention at the event just by showing up. The outfit was tame, by her standards. (The woman has worn telephones and lobsters on her head, for crying out loud.) If she had shown up in a pencil skirt and cardigan the paparazzi would have been there, taking her picture, commenting on her choice of outfit, etc. If she had shown up with a lobster on her head and hot pants the paparazzi would have been there, taking her picture, commenting on her choice of outfit, etc.
I've honestly never thought of a graduation as a "my time to shine" type of event. It's been reported that her sister was ok with her outfit. If I had been a graduate I would have thought it was cool as heck that Lady Gaga was there. I haven't heard any reports from actual students that they were upset. And honestly, the only people that care about your graduation are the friends and family you invite. Their eyes are still on you regardless of what anyone else is wearing.
Every college graduation I've attended has had a whole bunch of crazy, attention seeking mortarboards and I've always just laughed at those and never thought they were stealing the thunder of the person I was there to see.