I think you're not reading enough into small details.

I'm not saying that your ideas are not possible. I'm saying, what would be the point of it? Wouldn't it have been easier just to write: "Harry caught fire and went out and blazed up somewhere else; and just like that he, McGonagall, and the Headmaster, and the unconscious form of Hermione Granger held in the Headmaster’s arms, were occupying another place; with Fawkes above them all." ?

I think it would have been easier. So why wouldn't he have written that, if it won't be relevant?