The bolded part is in section 14 dealing with discounts. Nothing to do with upgrades. I suspect all non-discountable fars wil have the same section and may make most cheap fares (and possibly all web fares) unupgradeable!
I think you are correct that they should not have allowed the discount code rather than deny the upgrade.
May be they realized that mistake and rather than void the discount and ask for more money, they are trying to hit him up for a change fee or for an upsell to another fare instead and hence the change in story.
Since the OP is willing to forgo the discount, the right thing for AA to do is to first allow the upgrade with no changes (for screwing up on this one and giving him a run around) and if they want to be small asses, remove the discount and then allow the upgrade. Knowing AA, I wouldn't be surprised if they threatened to remove the discount and then refused the upgrade waitlisting or (refused to upgrade).
The OP may want to call up and ask them exactly where in the fare rules it says that upgrades are not allowed as you have the fare rules with you.