Were they now?
It wasn’t why they were actually leaving but they were right in saying it.
How could it be their reasoning if it wasn't the reason?
Yes. They were right about that. The Northern states had clearly not enforced the fugitive slave clause of the constitution in good faith.
How could a side in a contract dispute note that the other side had broken the contract even if that was not their motivation for wanting to get out of the contract? It happens all the time. Parties make their best legal argument even if that is not their actual motivation routinely.