>There is no way for you to verify that, and of course this is what a malicious VPN provider would claim as well. In short: the only safe assumption is that every VPN provider logs.

If the VPN provider has been ordered by a US court to produce log information, and they have appeared in court responding that it is not possible for them to do so as such logs do not exist, and the court has accepted this as true, that is adequate 'proof' in my eyes. It is something which puts them in the position of being extremely legally liable for in a way that advertising 'no logs' does not, since prosecution for false advertising is a joke.