Well the story is real (I remember when it first aired), and the Good Morning America footage is real from ABC. Basically "The Feed" looks like CBS's cheap and unfunny version of The Soup, making fun of things that happen on other shows. It's real (or was). That clip you posted is from 2011. I'm sure it was just an online only thing.
ETA: In case I was unclear, the text messages are not real, and he is not actually interacting with her. Like I said, there are a few shows like this out there (The Soup, Best Week Ever) that take clips from real shows and make fun of them.