No, the point was that they felt that because some states weren't happy about being compelling to help return runaway slaves, that South Carolina had been released from obligations.
We maintain that in every compact between two or more parties, the obligation is mutual; that the failure of one of the contracting parties to perform a material part of the agreement, entirely releases the obligation of the other; and that where no arbiter is provided, each party is remitted to his own judgment to determine the fact of failure, with all its consequences.(...)
Thus the constituted compact has been deliberately broken and disregarded by the non-slaveholding States, and the consequence follows that South Carolina is released from her obligation.
(Except, of course, that there was an arbiter provided--the Supreme Court)
I don't see that you're making an opposing point. Slave extradition (if that's what you call it) was the incident cited. Broken contracts and loss of sovereignty was the upshot.