It's not a rule in the sense that "no double-counting" is a rule (you won't find it anywhere in the rulebook), it's more of a soft suggestion. In practice, I've seen people follow it or disregard it to their heart's content. I personally follow it, because my philosophy is to upvote all constructive comments I reply to, and the other counter is literally helping me construct the chain.

But I mostly don't really worry about it either way, since comment karma doesn't count for much.