Courts can compel them to log this information, so all claims about not keeping logs are just theater. The second they're ordered to by a court in the US, they will.
So they can stop you from deleting existing logs, but they cannot require you to collect logs you aren't already collecting.
I have no idea how well this idea has been tested in court, but that's the theory on which providers who don't even have hard drives are relying.
Courts order individuals, businesses and officials to take actions as a matter of course: to stand trial, to comply with subpoenas, to adhere to a contract, to make restitution, and so on.
I am not deeply familiar with lawful intercept law and case law around national security letters (what little there is), but I would not gamble anything of value on the principle that courts cannot compel someone to take actions.
With an NSL, they could approach a company and require them to start collecting logs and also to not communicate about the new requirement, at which point a privacy-focused company's only choice would be to either comply or stop offering the VPN service entirely without saying why.
Without an NSL, the company would be free to communicate about why it was no longer offering the VPN service, or to announce that they were going to be logging from that point on, giving people an option to stop using the service if that's a problem for them.
But not having a hard drive in place currently, that prevents the courts from getting information about any activity before the court order or NSL is issued, as far as I can tell, which I guess is what those companies are counting on.
Not an easy business to be in, in any case.