Look at Brendan's first interview. He says Steven tied Teresa up and cut his finger in the process. Then he puts her in the back of her RAV4, stabbed her (the only place her blood was actually found), then drove the RAV4 to the location it was later found. He then transported her body back to the house to burn it.
I don't know why the prosecution didn't run with this version (his first version and the most believable) of his story.
Which interview was this from? There's no way that's the first. If he had said that in an interview he would have never been allowed back at school, and the first "big" interview that I'm aware of is when they pulled him from school and got him to say a bunch of nonsense about what happened in the bedroom, when the officer had to tell him Teresa was shot in the head.
He probably said that in a later interview after they couldn't find any of her blood (or DNA) in the bedroom so that needed him to create a new story that fit the evidence better.