This can be instantly disproved by examining the cases where valid warrants were presented to them by LEAs and they were unable to provide any user data.
Also they actually make it easy to use their services without providing any data - you can use them by paying Monero over tor, and the only thing identifying you is a short unique "identifying number" - no emails, no names, not even an account.
I find their gimmick of "buy a physical gift card from Amazon, scratch to reveal one-time code" to be pretty genius. It's just a bulk pile of cards, Amazon records you bought one but doesn't know which one (and the actual code is under a scratch-to-reveal surface).
Even if a three-letter agency intercepted your package and swapped your gift card with a known code, I believe Mullvad is not recording the connection between specific gift code and the account number.
You can also exchange unscratched gift cards with friends and strangers.
This can be instantly disproved by examining the cases where valid warrants were presented to them by LEAs and they were unable to provide any user data.