The police found blood matching Bill's type on the floor of Greg's guest bathroom.  They also discovered that the brakes of Greg's car had been tampered with.  From this and other evidence, the police reconstructed the following:

Bill was a debt ridden gambler who wanted to get one step closer to the fortune.  So earlier that fateful night, he tampered with the brakes on Greg's car.  Later, before Greg could use his car, Bill slipped and fell as he stepped out of Greg's shower, hitting his head and knocking himself out.  Greg bundled his unconscious friend into his car and headed for the hospital - but halfway there, Greg's brakes failed.  The car skidded around a sharp curve and plunged into a ravine.
Nathaniel, the last frat boy ended up with the whole fortune, which he promptly lost in bad investments. 

This is a combination murder and accidental death.  The fact that Bill accidentally died during the commission of his crime does not make his death a suicide.