Maybe because mentally handicapped people have no concept of hurting themselves or others with their movements and therefore do not consciously inhibit/downregulate/try to control the "neural drive" to their muscles? (Maybe this steers the thread back to the initial post).
My experience has been that old man strength is cited by underweight 15-18 dudes getting thoroughly boxed out on the basketball court by a 5'10" 220lb dad bod. Looking back, I think it's just weight and not relying on agility and athleticism.
This is probably a good example from a recreational context of my and Mr. Rowe's earlier comments. In farming, building, repairs, or other hands-on work contexts, it's "that old man can move/break apart way bigger things than I can - it's old man strength"...and it's because he knows how to do it the smart way, and because you never see him hurt himself moving something that's unreasonable, because he knows better. In both cases, the dumb young guy fails, but the old man's already failed enough that he knows better. He also probably knows how to use simple machines like levers a lot better.... It's not so much "old man strength" as it's "old man effectiveness", really.