Byron Farwell wrote an excellent biography on Jackson published in 1992. We know that reading was not taught during the class because Jackson, being a methodical man, taught the class from a syllabus that he designed and a copy of which survived, and reading was not on the agenda. The class itself did come under criticism from some local residents who threatened to go to the authorities and file charges. Those charges were for illegal assembly - it was illegal for slaves to assemple or be assembled - and not for teaching slaves to read.
I'm assuming the 1993 version is the same book.
What's really quite remarkable is that you managed to provide quite clear illustrations of argumentum ad ignorantiam in such a short post!!!
While in many places it was illegal to teach blacks to read, this was overlooked when the topic was Bible verses. Unlawful assembly was a violation that had nothing to do with the Bible. You also ignore the facts that Jackson admitted the classes violated the law, and the local resident who threatened him apologized immediately after.
You seem to be reading things with a strong bias, making you see things that aren't even on the page.