Sorry to hear about the down.
I think Apollo has the core of it, and if your lecturer didn't say to obviously use the brakes if you needed then that does seem to be an oversight. I'll put a clip in at the end from the Superbike UK's level 1 presentation -- should jump to 18:16 -- which is the clearest explanation of 'how' and 'why' to do the drill (including using the brakes if you must).
In my experience, the no-brake drill is best approached in a stepwise manner and helps tune entry speed and understanding of slowing from things other than the brakes (tire drag, lean angle, engine braking)... I can say I definitely cover the brakes but don't need to trail brake in for this drill (and a mild brake application mid turn can be done safely -- just be smooth and be open to needing to stand the bike up a bit, and definitely don't be adding brake while you're still trying to bend the bike over further).