But the whole point of that encounter is that the MC isn't smart enough to do the right thing. Both of the options she comes up with are wrong. The whole point of that first-day patrol is to show that the MC isn't that sharpest tool in the shed, so as to cut off at the pass later complaints in the porn portion of the game that "no one could be that dumb." Yes, someone can, at least in the game.
If this was a traffic stop simulator rather than a porn game, your point about what "ANY cop would do after a accident" would be spot-on (except that the testing would be done after the cop called an ambulance and got the dazed man to the hospital).