It seems pretty clear he's protecting the lady. And maybe also they are both trying to avoid hurting the husband/best friend.

I've sometimes thought of starting a rumour that it's all about Joe Hill, who was said to have an alibi which he didn't use because it would have meant betraying a lady. (Though in the witch-hunt atmosphere of the time it probably wouldn't have saved him anyway, even if he'd had a dozen alibis. There are modern day analogies to that as well.)