That's too-strong language. There's no legal obligation to respond to a DMCA claim—rather, failure to respond loses you safe-harbor immunity in that specific case. That's unpleasant, in the case the claim is actually substantive, and the claimants can afford attorneys.

It's an (IMHO) important distinction when talking about how corporations treat their clients, because otherwise you're assigning agency to the wrong actor. It's classic corporate gaslighting to say "we're sorry we're forced to do this" when, really, they're not—they simply do not highly value their business relationship with you.