> So you have access to other information, just not very trustworthy. This is equally visible to the liar; you don't have any information that they don't also

> So you have access to other information, just not very trustworthy. This is equally visible to the liar; you don't have any information that they don't also know about and can control for. [I already edited this in the original post for attempted clarity, apologies for any confusion]