I am jumping to conclusions it is true.
However say you really liked a man, and you were in the process of seeing if you could be in a relationship together. Then a single friend mentions "oh I see you know Bobby, he seems fantastic and we are both single, can you give him my number"
Why is it against etiquette to say "friend, I really like Bobby, and we are seeing where this is going to go, I hope you understand.My friend Mitch mentioned that he thought you had a lovely laugh and he's a doctor... would you like us all to go for drinks" I think that's fine to do, but I could be against etiquette there. I don't know.
In general, if you don't want to play matchmaker, I would say that you've been in the middle of situations like that before, and there was some negative fallout which you don't want to be a part of again. Just say you don't really feel comfortable with being in the middle of a relationship
where you could lose a friendship.
But I don't think we can lose sight of the specific example you provided in the OP. If you like the guy, I would just say that you were interested in him. Also, you said you don't understand why he hasn't asked you out yet. Have you done anything to pursue him? Let him know you are interested in him?
I don't think it would be all that fair to sit by, waiting for him to make the moves, while you do nothing to pursue it, but also don't allow any of your other girlfriends to pursue it either.
But in any case, she hasn't even indicated she wants to date him. It's a business contact.