But if you do hold an AOC you can't conduct lessons on an AOC flight!!
Not strictly true.
Taking the multi crew example, both pilots have to be rated i.e. have the raying in their licence.
However, it is normal practice for line training to be completed with passengers aboard.
More importantly, if a crewmember does not have 3 take-off and landings in the past 90 days they can fly in the period between 90 and 120 days with a TRI/TRE and passengers on board.
Single crew operators will have similar and aside from base checks you will not flind many training flights that do not have passengers on board (unless business is poor).