It makes sense to me. Most J revenue is from paid business travel. Corporate travel policies usually restrict on class of service rather than price. So no one can buy something called "first class", but you can give them a really good J and charge plenty. It's optics.

Regarding the actual topic at hand, if Jon says it isn't true, I'm inclined to think it isn't true, but on the other hand, the substance of this rumor is completely logical and expected, and I don't see what incentive either the OP or the AAgent they spoke to (who, from what the OP noted with respect to the outcome of his flight booking, seemed very competent) had to misstate the truth. Especially because what the AAgent said wasn't the usual hand-wavy "Them's the rules" type response, but an explicit reference to a training program. Certainly piques my curiosity. Guess we'll see.!