See, only incompetent dunces violate TFR's. Sarcasm, of course.
The reality is that very proficient pilots, with much experience, will overlook what seems to be a minor paper work step, and get into trouble. Did the Army provide a GPS with TFR capability? Did it fail to update? Did they get a briefing before launching down the river on a standard flight pattern? If so, did the briefer fail to notify him of the local Notice To Airman? Did they file a VFR flight plan, and get it accepted by an FAA person who should have advised that the plan would violate the TFR?
There are a lot of questions here, and it might not be primarily the instructor's failure.
I know that every one of those has happened in the Washington DC airspace, to pilots that I have talked to following the event.
I have a lot of sympathy for all who are responsible for this happening, and it is clear that they did not do it on purpose.