Yes it talked about fugitive slave laws and that was specifically cited in the document. But the point was the loss of sovereignty.
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)
What about the lost sovereignty of the Northern states? Why couldn't they, in their sovereign role, require extradition hearings, jury trials, legal representation, and the life for fugitive slaves? A white fugitive would be entitled to such protection. But the overreaching federal government, at the behest of the slave states, stripped them of their right to do so. I guess states's rights is for southern states only.
What does sovereignty have to do with the return of runaway slaves from other states? If Brazil refuses to extradite some criminal, we don't argue that Brazil has undermined our sovereignty. You can argue property rights and their equal protection, but I fail to see how you can argue sovereignty. You're actually requiring that free states surrender sovereignty in order to support the slave system.