What I find interesting though is the fact that you must vent a toilet
*downstream* of the fixture. Totally counter-intuitive if you think
that the purpose is to provide air for draining. The slug of water has
to run a few feet before it gets to the vent. My plumber told me we
can't put the vent behind the toilet (upstream), but he didn't say
why. (probably doesn't know the why). I'd love to know why that is.

I think it's because when you flush the toilet, you get a sudden rush of
water that would go upstream and downstream. Since there's more than just
water in there, you could get debris pushed upstream, which could
potentially block the vent.

By placing the vent downstream, every time you flush, you're washing away
any debris left behind from the previous flush, thus keeping the vent line
clear.

This is the same reason codes do not allow horizontal venting from the
drain line. The vent has to come off the drain by at least 45 degrees so
there's less risk of it being plugged up.

Of course, assuming you have space in the joist bay, you could vent off the
drain "downstream", then run the vent back towards the wall to go up and
out.

Anthony