Incorrect. South Carolina was taken out by her legislature. Missouri was. North Carolina was. Virgninia was, too.
Missouri was. A rump faction of the Missouri legislature, on the run from Union troops, voted MO out of the Union. While the CSA considered MO a Confederate state, most Missourians did not. Probably more than twice as many fought for the Union than for the CSA. A similar scenario played out in Kentucky.
North Carolina was. Nope. "We, the people of the State of North Carolina in convention assembled..."
Virgninia was, too. Nope, again. I happen to be fairly familiar with the Virginia Convention, as it voted secession down by over 2:1 before Sumter, then reversed itself by the same proportion after Sumter.
The political theory of the time was that a Convention spoke directly with the voice of the People, whereas legislatures were composed of politicians. This theory appears to have largely disappeared without a trace. Also I believe Conventions were held to ratify the USA Constitution, so the theory was that a Convention was needed to secede from the USA.