After I slept on this, a way to illustrate this confusion occurred to me.
Picture a scenario where you are in school studying two subjects which are not coming naturally for you. Say, Trigonometry and history. Now, I know a lot of students who successfully work both of these subjects into a single school day. And this is similar to what I was saying about parallel sessions. But now picture combining these into one single class session that is covering both at the same time. Its even more clear how confusing this would be if it were combined into one lecture. After just a few minutes most of us wouldnt know what the instructor was talking about! That is similar to trying to teach two different behaviors in one session.
I also realized I was not sure if Fred was referring to "killing 2 birds" in one single training session, or in parallel ones. If they are parallel sessions it would work just fine.