I see. I'd assumed that you were competing primarily on ease of use and pleasant UX, which if that were the case, you'd want potential customers to see what you are doing.
If it's actually about trust, it sounds like word of mouth is actually more important to you. It just seems a shame that you'd be extremely unlikely to get my business (assuming I were looking for such a service) simply because I wouldn't be able to evaluate your service without handing over data that I'm loathe to spread around, particularly for services I might not actually want.
[By the way, another model that might work for website checking as well as restricting the number of sites is delaying the notifications on the free account after the first week. Anyone who really wants the service almost certainly needs the notification immediately. It also gives you another excuse to email them 'by the way, your premium notification speed add on is expiring, upgrade to a full account to keep your instant notifications....]