I don’t know if I believe that. It’s a paid service, so the only way to enforce that unpaid users cannot search is to take a search request and check if it is coming from your account. Same with basic things like rate limiting requests. You literally need to associate your requests to an account to make basic functionality like this work.
If they do this but just don’t log it, then that means there is no way for their devs to ever debug issues users have or to monitor their services. I’m highly skeptical.
Also, “trust us” is something I’ve heard too many times.