The phrase in the title is a common trope that comes up when VPN services are discussed. While this statement is technically correct, it can be misleading, as it implies that all providers handle law enforcement requests and prepare for worst case scenarios similarly, so their conduct cannot be a differentiating factor when you evaluate them.
As others have said, Mullvad is pretty close to (if not at) 100% guarantee… No personal info whatsoever is required to be given when you sign up (including email address or payment information; you can use Monero if you want), so there isn’t really anything that they could give to authorities even if they wanted.
Even if they did keep logs (which im 99.9% sure they don’t), all that would show is an IP address, and from what I understand based on past precedent, that is not enough to identify a person on its own. But IANAL.