It's misleading even then, when you look at the actual complaints of the states (as expressed in their declarations of independence). For example, most of them complained about the free states' pushback to the Fugitive Slave Act, which was also a states' rights issue - but the one where interests of the slaveholders aligned with a stronger federal government strong-arming states; and they didn't have any qualms about that.

Similarly, in the Confederate constitution, there were some provisions added that specifically restricted the ability of the states to handle slavery in their jurisdiction - e.g. the "right of transit and sojourn" (which essentially meant that free states were forced to respect the "property right" of any slave-owning citizen of another state who comes to reside there) - this, of course, was in response to Dred Scott.