I find the people who use the "Pain says something is wrong" argument are the ones who are less in shape anyways. Pain is the great signifier of something being wrong, but some use to as a reason to not do a thing.
Well, I have trainers who are in great shape and say that, so. . . .
In the general public, there's a misperception about pain
always signaling injury, which of course is not always the case. In my husband's case, the damaged spinal discs are as injured as they're going to get, so when his pain intensifies, it's not a signal of more injury (hence, he's "doing something" to himself), but a signal of the sciatic nerve being compressed more, which happens for a variety of reasons, none of them being increased injury to the discs, themselves. As his physiotherapist says, "Pain is a great liar."
Still, if the pain is so bad that he can barely walk, then that's hardly heading in the right direction, eh?
So we have to be careful to interpret pain in the correct way, and that means being educated about what the signals we're receiving really mean, and what to do about them. As you say, many people interpret pain as a sign to stop moving altogether, but of course that leads to muscle weakness, which further exacerbates pain, which leads to a further decrease in activity . . . which keeps that circle going round and round. In almost every case, the answer is not to stop moving, but to keep moving in the correct way.