Flyer,
Parsonage, or housing allowance, almost never involves the Yeshiva directly paying the housing expenses of those who are eligible for parsonage (Clergy), or even providing them with a house. The checklist that the Agudah put together (and this is old, I first saw it probably more than 15 years ago) was so that the amount of parsonage can be determined and supported. The amount of parsonage allowed is the lesser of eligible housing costs or the fair value of rental.
Qualified Tuition Reduction, QTR, is a completely different benefit and is specifically for educational institutions and their employees. It is a non-taxable benefit that is explicit in the IRC. The benefit can be used to pay for education expenses at the school itself or even at other schools, for the employee or the family members of the employee. Often times there is a requirement for there to be reciprocating agreements between institutions and that is why it is not feasible in every case.
What is clear is the Chiam was slightly aware of such programs, and just blathered on because it bothers him that a Rebbi also gets consideration from the tuition committee when determining the tuition the Rebbi has to pay for his children. But he clearly did not know the actual details and three days after being told that his post did not make sense, was able to google up a small amount of the details.