Personally I'd be a bit cautious about putting in your own license plate number there. I can't find any immediate red flags, but it just seems like good opsec to not potentially expose your own plate if they're not being honest about not storing queries.

If anyone else knows more about how legit the group running that site is, feel free to chime in. They are funded by The Alternative Newsweekly Foundation, who are members of the Association of Alternative News Media, but I don't know much about either, and the wiki entry for it is pretty sparse.