Well it does not make sense to me – if they worded the offer as "stay 3 nights and get 33% off" the amount paid would be the same but by their logic you would get the credit for all nights. Pushing it to the other extreme they could also advertise "stay 3 nights FREE*! (* subject to a 2 night corp rate booking fee)" and award zero night credit.

This is absurd. Nothing's "free" if you have to buy something to get it… All the nights were paid, they are just shuffling the money creatively…