After tentatively poking at this guy a couple of times, I went around the boulder to investigate something else (a huge black widow.)
When I cam back around, he had run down to a ledge and was hanging motionless by one foot, seemingly caught in a cobweb. I picked him up without any trouble.
I put him back on the rock (in a sunny spot), but he still didn't move for about half a minute. (I was worried he was in shock, or perhaps had been bitten by a spider.) Finally he skittered a couple of inches -- so he was okay.
I think it was a defensive behavior, but I'm not sure whether it was in response to me or to the cobweb.