Shoutbox

I don't think he's talking about chat logs on his computer but on the server, that the gateway/proxy is recording his messages.

The only way to get around it is trying to get access to the web without this proxy and if that's not possible then use encryption.

But encryption is only possible if the other person receiving your messages also has the means to decrypt this message, so it might not work because your contacts don't have this software and don't want to install it just for you.