“So how did the black sweatshirts wind up on the parking lot outside the vehicle??? and why were all four doors opened???”
There are other possible answers than to believe the police enforcement contaminated the scene - which is what your narrative requires.
Here is one more thing. At the time they get to the school they don’t know that the owner of the car is dead.
So THEREFORE there are rules to follow as it pertains to searching an immobile car that isn’t going to go anywhere.
We're waiting ..............