What is the story behind SNL with Taylor Swift?

It said in people that Taylor Swift wrote the song herself. Penelope is just a character they've used before that is really annoying and I guess tries to one-up everyone. In one she was saying how her best friends were a tomato and Liza Minelli and everyone is like "what?!" and then liza minelli (fake) came in and was like you me and tomato are going out! yeah, it is just an annoying character