I am not familiar with those cars, but it'* not inconceivable for GM to design it so that the ignition kills if the oil pressure drops. It'* something I would appreciate.
The list of other things it could be on that car would be relatively short. If you pull the sensor out, crank the engine a bit, and have oil everywhere, than you could almost bet money on it. Given that you can likely get it at a local parts chain for $15 (they may need to special order it, or order it from Rockauto) it'* a relatively cheap part to throw at it.