I think the difference is that you should write in their world but not write their characters — or, if you do, make sure you do so with a very light hand. Like I said in the write-up, if you write their characters they’re going to be put into a position where now they’re evaluating how well you did so…and that’s a tall order, and more than the applicant should be attempting.
It’s like someone who applies with a submission in the Dragon Age world who not only includes the character Alistair but makes their submission about Alistair (or he plays a very central role in their story). As Alistair’s writer, I’ll suddenly find myself evaluating how well they wrote his voice rather than just how well they wrote, and I’ll find myself cringing every time I encounter Alistair’s story going somewhere I don’t think it belongs.
I wouldn’t state that too definitively, however, as I imagine it’s possible to do it well and also possible there are writers out there who wouldn’t mind at all if someone wrote their characters. I just say it as a point of caution.