Nurse Freddie's clue

Midway through the movie two of the doctors and three nurses are gathered in the nurses' quarters. Freddie says something like, "I've had a thought about that hole in the gown, I've just realized something that may be important."

She's just about to tell them what that something is when Trevor Howard says, "Shut up! Don't tell anybody but the Inspector!"

This always bugs me. Not one of them says, "Wait a minute, if she keeps it to herself until later she could be in terrible danger. The safest thing she can do is speak out. The murderer then has to kill all of us to keep the clue from coming out."

It's a small point in a wonderful film but it's always nagged at me. Still, I guess if characters always acted sensibly we'd have no thrillers!