That argument seems a bit disingenuous to me considering that some states secession declarations specifically list grievances against other states for exercising their own states rights. Specifically laws that interfered with the enforcement of the Fugitive Slave act and limiting the southerners ability to transport slaves through their states.
For example, the Texas succession statement calls out specific northern states for exercising their our states rights in these matters.
"The States of Maine, Vermont, New Hampshire, Connecticut, Rhode Island, Massachusetts, New York, Pennsylvania, Ohio, Wisconsin, Michigan and Iowa, by solemn legislative enactments, have deliberately, directly or indirectly violated the 3rd clause of the 2nd section of the 4th article [the fugitive slave clause] of the federal constitution, and laws passed in pursuance thereof; thereby annulling a material provision of the compact, designed by its framers to perpetuate the amity between the members of the confederacy and to secure the rights of the slave-holding States in their domestic institutions-- a provision founded in justice and wisdom, and without the enforcement of which the compact fails to accomplish the object of its creation. Some of those States have imposed high fines and degrading penalties upon any of their citizens or officers who may carry out in good faith that provision of the compact, or the federal laws enacted in accordance therewith."
Some would say the Confederacy fought against states rights (the rights of norther states) rather than for them.