I agree with what you've said, but word of caution, this has to be handled with a bit of finesse, I think. I almost got passed over for a job because I said this and gave the recruiter the impression I wasn't that interested.
I had a acquaintance on another team who mentioned it to me, and I did a little "damage control" with the hiring manager. I got a great offer in the end -- and it was a great job -- but without that contact I would probably have whiffed it.