The goal behind a psychological proof is simply to convince most people of something. And that's all that's required. A psychological proof may be complete nonsense but as long as it convinces most people—namely, those of average intelligence—then it can be considered a success.
Such proofs can be useful on the web, particularly when a proof that would be convincing to intelligent experts is impossible. Moreover, such proofs need not be deceptive (e.g., as with phishing). You could have a nonsensical/weak psychological proof to convince most people of something that is actually true anyway, so no harm done.
As an application of psychological proofs on the web, consider "reverse CAPTCHAs" within the context of chatbots. It is important to give people chatting with chatbots some confidence that *all* the bot replies are really bot replies—and not something typed in by a human watching the chat.
The problem is to somehow convince most people that you are really a chatbot and not a human. The method used should give them more confidence than simply telling them so.
While chatting with the bot from chatbotgame.com, you can get this confidence by clicking "Convince me you're a bot!". The idea is to show you the rule/method that was used to generate each bot response. Note that you can see rule usage in other chats by clicking accepted/rejected. This gives you more confidence that a rule was submitted prior to seeing its bot response in your chat.
I would be interested in knowing about other uses of psychological proofs on the web to convince most people of something that is true anyway.