I’ll play devils advocate here and ask that if the touch and go was so dorked up that you had to take the airplane on the runway and do a Bob Hoover style save to keep the jet from departing, could you not see that developing on short final/in the flare?
If the student landed with a brake locked and the airplane snapped into the dirt or something, then I’d say you had no chance to prevent that. Given the info you presented, it’s definitely in “it depends” territory.
Personally, it takes an unbelievable amount of buffonery to give a downgrade let alone a Q3, but I’ve seen extreme examples in the other direction. Sounds like you may have fallen under that side of the spectrum.