Yes.
There's not a lot of middle ground between "You're so paranoid-- what are you so worried about all the time, because we don't see {name} as sick... you're damaging him/her with your paranoia," and "wow-- you sure take {name} to the hospital a lot. Maybe you should do some things different, you know?"
Perilously little ground between those two, and honestly, it's not like you can't get BOTH reactions from different people in your life.