Poison damage is dealt at the beginning of the attack phase.
Would this prevent healing from purify (which is done at the same time as poison damage)?
I am not sure. Thinking critically, I would say that that is healing not negative damage so yes it would work. But in the interst of "You can't have it both ways," it could be a no. I don't know how the game treats Purify counters. That is the deciding factor right there.
As blarp found out in the deck bearing his name, purify used to be treated like spell damage. This was evident by the ability of a mirror shield to deflect it back at the opponent.
Apparently, this is no longer so.
Purify is treated separately now (hence the lack of mirror shields in the current incarnation of the blarp deck).
I believe most healing effects from cards are as well.
Negative damage is indeed distinct from healing.
This is evident if you attack an mirror wielding opponent with an antimattered psion. The negative damage gets bounced back and heals you.
Ultimately, I think its your call as a designer, but right now, I would say if you are looking purely at stoping damage, then it makes sense that negative damage gets blocked, but other healing types go through.