What would have happened, to the hospital's part, if they had declared that you were not intoxicated and you should not have been brought to the hospital, and sent you on your way? Would the police have had to justify dragging you to the hospital, and pay for your examination? I suspect that going along with the police may have been the decision with the simplest and most profitable outcome for everybody (apart from you) and that the hospital side was incetivised to go along with police's story rather than against, but I am not sure how things there typically work in such cases.