Assuming for a minute he did that (which, I hasten to add, I do not believe) - would he be doing so on an airway ??
Since we're all theorizing here (see lenstrad's comments), I thought I'd toss that in. I assume the box will indicate if either altimeter had been set correctly, thus perhaps making either pilot assume incorrectly there was no traffic ahead of them (and the bizjet assume a little demonstration could be carried on quite safely at his altitude). You are dealing with what I assume are two flight decks full of very professional pilots who aren't going to take chances unless their instrumentation gives them false readings.
I keep wondering about that "shadow," that "thing" the bizjet saw above him.