But what if person that signs it, lies about it? It shouldn't be hard to use tor, new wallet, and that's all. So why signed messages are so trusted?
Signing a message is only valid if the address you are signing from is older than 3 months. There is no way you can lie about it because the signature muat be verified first before someone accepts it. They can verify if ou really signed the address using their own client or coinig and blocktrail.
New wallet is not accepted .