The choice you made was between the two options they gave you. Either outcome is part of their system, and perfectly fine by them. There was also third option wherein you notify them that the debt is invalid because no services were rendered, and that it is not your responsibility to convince their systems and processes of that fact.
Yup, and in the end, I'm fine with the choice I made - pay them and then let people know how awful the experience was. This has been worth $2 for me, I hope it was worth $2 for them.