They are correct. I just have these doubts from time to time and start shouting "Help! Help!".
Don't worry! When you say "fine", they are correct! That's what "correct" means.
Thanks Milky and Tdol,
The "monsters" were actually the topic of a question.
I think the sentence was:
"I'd hate to have my team lose."
or something of the sort.
"I had something terrible happen to me the other day."
seems to be a common one.
But it seems to me that Tdol's sentence is of a different sort. In it "had" seems to be causative. It is like, "I asked him to wait."
I don't even think it can really mean "I kept him waiting". It really sounds to me like you asked him or her to wait. Am I right?