I've sent DMCA takedown notices. A garage band could too. You don't have to prove you're the author to send a takedown notice, you merely have to assert it.
And in the case above you'd have to sue the party claiming to have copyright on your creation but that's optional.
But if somebody sent a take-down request for my work, and it happened because they had sent a million take-down requests to everything on the internet matching a string search, then I would begrudge them and seek to penalize them. They would have done so KNOWING that a huge percentage of them would be wrong, but deeming it acceptable since it's no cost to them.