I see their point only as far as the question of whether you would remember the patter for the exercises and whether you can remember how to draw out the lift curve and relate it to the drag curves to come up with the L/D curve. That's where I see it ending. Any good teacher knows they need to know the material, so would at least go back and read some literature before hopping into an airplane or classroom.
Besides, a pilot who has spent years trying to figure out how best to teach at the airline level - which as you probably well know means having to often reach back into the old basics bag - and get through to certain students means we have to keep up with the basics anyways. Lord knows the last ground school I taught I had to go right back to basic prop theory and build from there...the student had been taught completely wrong on day one! If that scenario, which happens on a daily basis, does not prove airline instructors meet the minimum requirement, well...I'm not sure what would.
I digress. That's why I was wondering before if maybe a TRE/TRI format could help those pilots to come back to the flight schools and clubs. At the moment with no certification process there is nothing for Transport to gauge an instructor pilot to a minimum standard. But throw a certification at our airline instructors, make them prove at certain intervals that they remember the basics (kind of like how an ACP has to do their renewals) and there would be ongoing proof that the guy had the theory and experience to become a flight instructor again.
Not saying that this needs to be the only result from a TRE/TRI format, but certainly a benefit thereof.