We agree. A few Confederate soldiers did get out of the Yankee prisons by signing the parole, but most didn't and consequently they stayed in prison. Signing paroles was not a condition of the general prisoner exchanges.
I don't claim to know much about this, but didn't Grant stop paroles based on widespread abuse by the CSA? The garrison of Vicksburg was paroled and most of them were back under arms very quickly, as I recall.
Walt