States right to do what?
The disagreement was with other states that were actively encouraging non-enforcement of federal laws, as well as with the incoming party of abolitionists.
The Fugitive Slave Laws were federal laws and as such the states could not be compelled to enforce them (Prigg v. Pennsylvania). The federal government enforced those laws to the best of its ability. Every time the states enacted laws meant to hinder the enforcement of the fugitive slave laws, the courts struck them down.
And if the issue was Northern state interference with the enforcement of the fugitive slave laws then why didn't the states rebel in the 1840's or 1850's? Why did it take the election of a president opposed to the expansion of slavery to cause their actions?
That is verified in the secession documents.
The fact that the South rebelled to protect slavery is also verified in the secession documents, as well as speeches and writings of Southern leaders of the time.