And here's why I asked
If I ever gave any particular thought to the phrase "A rolling stone gathers no moss," I think I assumed that it had to do with staying active so you didn't get bogged down, kind of like the opposite of being a couch potato or a knick-knack that just gathers dust.
Apparently, though, it originally meant something closer to another proverb that's not really in use any more: A frequently replanted tree yields little fruit. It's more of a "Bloom where you're planted" kind of thing (or more bluntly, "If you keep moving all the dang time, you won't have roots anywhere and you'll never succeed, so settle down already!"). In this case, the moss indicates good things, like wealth and success. Pretty much the opposite of what I thought. But I'm not the only one who interpreted it my way. Others, according to Wikipedia, use it to indicate someone who wanders around to avoid picking up responsibilities and cares.
Perhaps a better axiom would be "A vaguely worded proverb gathers multiple interpretations," but that's probably not quite snappy enough to become an old saw.