Of course, if the cops do push back at the hospital,
the medical staff can let be known that cops will be last on
the treatment list if they need it.
I saw an episode of COPS once where a police officer pulled over a nurse for a traffic infraction of one kind or another.
The cop talked with her briefly, then let her go on her way. No ticket was issued.
The cop looked at the camera and said something like, “someday I might be injured in the line of duty, and I would not want the nurses who are treating me to be mad at me” (or similar words).