Yes, I agree.
In the good on you BBC version, maybe was because it fit better to the quartet version for that session, in the other case, maybe we don't have the full songs... Maybe better wait until Friday but I agree, usually it sounds better arranged when drums come later, I do it a lot when playing with friends, I wait until they play some verses and then I start playing drums, first softly and at the next verse with snare. It's always a winning!