I don't have any special knowledge of this crash, though I did see the interview of the witness, who said that the aircraft "spiraled down until it hit with a thud."
That sounds to me like it could be a spin. With four people in a 172, on a planned sightseeing trip of more than an hour, it's likely that the fuel tanks carried a larger quantity of fuel. That would very likely result in an aircraft at a weight heavier that the 2100 pounds, and C of G further aft, than that required for the utility category. The aircraft would have very different spin recovery characteristics if it were beyond the W&B limits for the utility category.
During my spin testing of larger Cessnas I have found that aft C of G's can require a well executed spin recovery technique to get a prompt recovery. Casual or poor technique can certainly prolong the recovery.
Though this is very sad, I can't stop wondering if youthful exuberance resulted in the addition of a few "maneuvers" to a sightseeing flight. It would not be the first time....