This is hypothetical - the glasses don't fact-check what people say, they somehow detect willful deception, like people expect polygraphs to do, but with high accuracy. Would people welcome these, fear them, object on privacy grounds? I think it would be very contentious. Would people feel different if they only fed the information to the wearer but didn't record or send it anywhere? What exactly would the issues be?
To sum that up, are you saying people would find reasons to disbelieve that their heroes and icons are lying? I was thinking more along the lines of personal contact - everyday conversations, business deals, etc.