I agree completely with the sentiment of this article (although the title is perhaps a bit overblown): you shouldn’t need a separate API—that’s what you’re existing URL structure should be.
I’m not entirely sure that content negotiation is the best way to go when it comes to serving up different representations: there’s a real value in being able to paste a URL into a browser window to get back a JSON or XML representation of a resource.
But this is spot-on about the ludicrous over-engineered complexity of most APIs. It’s ridiculous that I can enter a URL into a browser window to get an HTML representation of my latest tweets, but I have to sign up for an API key and jump through OAuth hoops, and agree to display the results in a specific way if I want to get a JSON representation of the same content. Ludicrous!