I think that 4e D&D is a variant of D&D. And "fail forward" is a key idea in 4e D&D, especially skill challenge resolution.Let me try something new. In the games where these fail forward techniques are properly implemented (which exclude all variants of D&D with siblings), the "skills" do not represent the character's innate ability to do things.
And Burning Wheel is a game in which "fail forward" is key an in which skills do represent a character's innate ability to do things.
So I think both the assertions I've quoted are not correct.