Basically it could be that he's not "lying" by speaking a half-truth, e.g. if he didn't resign then the writing was on the wall that he would have otherwise been fired.
Some people's memories aren't very reliable, people who develop lying as a habit, who weave webs of lies - "the lies we weave when we learn to deceive" - are especially not going to be reliable with their recall; and you can get signs of this based on how they respond or react to questions or engagement.