As far as the Greeneville convention, you're certainly correct.
The Southern States enjoyed a Natural Right to Secede from the US Federal Government, and Greene County enjoyed a Natural Right to Secede from Tennessee and seek re-admission to the USA.
Obviously, it was morally wrong for Tennessee to deny Greene County's Natural Right of Secession, just as it was morally wrong for the US Federal Government to deny the Southern States' Natural Right of Secession.
Glad we're in complete agreement.
The Greeneville convention didn't only speak for Greene County, but the whole of East Tennessee. The problem for the Confederates was that there was a vital railroad from the Deep South to Virginia running through the region. Also the region contained the CSA's only domestic copper source and an important percentage of southern food agriculture.