Coppola had to play fast and loose with that scene or the movie would have been 5 hours long. There's no way that a bunch of private detectives could have been assembled and transported to the hospital in the few minutes which the film allows.
I don't think Michael's bodyguards had anything to do with it.
But if Michael's body guards had followed him, surely Michael would have asked them to stand out in front of the building, or at his father's bedside.
