You know, I always figured that was just a funny story people told. Reading what @the_lucas said about his cat though, maybe there's something to it. Animals are tuned into body language and energy in a way we just aren't. It makes sense they'd pick up on the shift when a muscle finally lets go. Guess I shouldn't be so quick to write off the little helpers.
No kidding, my cat does the same thing when I'm working on my partner's shoulders. He'll purr like crazy when the tension starts to melt away, but he goes totally quiet if I'm pressing on a spot that's still locked up. It's wild how animals just seem to know. I started using him as a little fuzzy biofeedback machine.