I've done it the way that it has been described, and I've plopped the whole shebang in the primary. The way that was described is certainly easier and less time intensive, but the other way is fine too.
You'll just need to rack more often to get the pieces-parts out.
I've "primary-transferred" (what i call it) where after fermentation has started and the must is all goopy, I just take the one primary, and slowly dump it over a large sieve into another. At this point, oxygen is okay, and so I've never had any problems with it. This takes an hour or so, depending on what's left of the pulp, and how fine your sieve is. I let the sieve sit on the (now empty) primary at least overnight, and then dump the remaining juice that is in there into the "receiving" primary. I let fermentation go a couple of days longer in the "receiving" primary, and then transfer to a carboy.
I don't know if this is "correct" winemaking procedure, but it's the one I've used. And it works.