Then Sue, Johnny

Now, I'm not a lawyer like some people but, so far as I know, a story which is "false" and "made up"  rises to the level of actual malice on the part of a news organization.  One might think that a highly-successful litigator might well take action against a news organization which was spreading a vicious and entirely untrue libel across the entire world.

I'm just saying.  It's probably also worth reading his exact words carefully:

"The story is false. It's completely untrue, ridiculous"

"I've been in love with the same women for 30-plus years and as anybody who's been around us knows, she's an extraordinary human being, warm, loving, beautiful, sexy and as good a person as I have ever known"

Just reading it very carefully - I don't see anywhere where he specifically denies any sort of relationship with the woman in question.  And, further, reading all of this in a lawyerly way, "the story is false" could mean any number of things.  Similarly, telling us how much he loves his wife isn't actually all that relevant to the accusation at hand.