On the 747-400:
Fuel load more than approx 120T: The Centre Tank feeds the outboard engines during take-off (and landing!)* and the inboard engines feed from their respective wing tanks.
*Any time the flaps are extended. (Wings hold about 110T but there might be a restriction on Centre Pump usage with low fuel levels in the Centre Tank.)
Fuel load 53T to 120T: All engines feed from the inboard wing tanks during take-off and landing.
Fuel load less than 53T: Each engine feeds from its respective wing tank during take-off and landing.
Also, as far as I remember, there was no prohibition on crossfeeding fuel during take-off and landing, if it was required.
So, to answer your question; I don't think your instructor is correct for "all aircraft".