Just read the Fourth Amendment with my eight-year old after she saw the video (Mom is an ER nurse).
SHE (the eight-year old) understands this perfectly well.
The right of the People to be secure in their persons...no warrants shall issue except upon probable cause...
This is NOT complicated.
Then get a warrant. The nurse and the hospital has to CYA, because they can and will get sued and their insurance companies will pay out the nose and their rates go up. Cops get sued and the taxpayers pay for their mistakes so what is the downside for them if they screw up?