They have logs, they just don't keep them very long. (Allegedly.) So in theory, while they might not have logs for a past incident if it's been long enough, they most certainly have logs in very short term and/or can tell who's connected to what at the present time. So while many copyright actors will be too slow to get a hold of said logs, a government actor with significant interest will.

The biggest issue for me is that VPN providers have given me no particular reason to trust them. If I already have reasons to distrust large international corporations that say they care about my privacy, why would I go trust one I've never heard of on the Internet that says it cares about my privacy?