Did the South view it as a disingenuous strategy to maintain the loyalty of the slave border states, or were they worried about giving legitimacy to the Northern government by partaking in its legislature?
For those interested in what the Corwin Amendment was, here is a link to the Wikipedia page, which includes multiple citations for the text of the Amendment:
Mods, I posted this because I assume a lot of people are like me and have never heard of the Corwin Amendment. I know the rules, and I know that this post doesn't really qualify as a legitimate answer.