I will ask Avellone how it works but if I have to guess (if I were the designer), I'd check for both. For example, to pass a certain check you'd need Honesty more than 3 and Deception less than 2.
In general though, if you lied to 9 men but were always honest with one guy, this guy would say that you're the most honest person you've ever met and would probably think that those 9 guys are making shit up.
Unfortunately, it's more like
Watcher has 2 honest, 3 deceptive
Conversation has 5 options:
(3 deceptive): "You know I lie a lot, I will lie to John for you."
(2 honest): "You know I am honest, and I will help you."
(2 aggressive): "Requirement not met."
(No check): "How can I convince you that I'll do it?"
So you get to choose whether in this case you want to use your reputation for being deceptive or for being honest. I had that case, when ambushed by Thaos' wizard lady at the beginning of Act 3, where I could convince her and her goons to surrender - and either option worked.