Walt is willing to swear on the Bible he's not having an affair

This part from season 2 (episode 4) has intrigued me for years. Walter White, despite being a liar and criminal, is technically not lying when Skylar confronts him. He specifically said that "I'm not having an affair", and he's willing to swear on the Bible that it's the truth.

So technically Walt is not lying here. He really isn't having an affair.

But why does he feel the need to tell a truth in this scene? He's already a criminal, already lied to his wife about many things and will not hesitate to keep lying to her. And yet, in this particular sentence, he chooses to tell the truth.

My theory is that, Walt is unable to lie if he's really swearing on the Bible!

Even a liar/scumbag/asshole (however you want to call him) like Walt has his principles. He can't swear on the Bible that he doesn't have a second phone. He can't swear on the Bible that the ringtone Skylar previously heard was his alarm clock. He can't swear these things because they are not true. However, he can swear that he's not having an affair, which is the truth.