Werepyres vs. No Werepyres

In Stephenie Meyer's Twilight world, would vampire/werewolf be able to exist? If not, why? And if so, how?

My opinion: I don't think hybrids would pan out under SM's conditions. If the werewolves and vampires have the whole smell thing just to keep them away from each other, wouldn't they have some other mechanisms? I think the werewolves would have something medically preventing them from the vampire venom. Either they would be allergic to the venom and die, or be immune to it and nothing would happen. And since werewolf-ism (lol) is genetic and not infectious, a vampire couldn't be turned into a werewolf.
The only way I can see a hybrid happening is if someone like Jacob in Twilight (going to be a werewolf but not yet) were transformed into a vampire, and later the werewolf symptoms would start to happen. However, in SM's world, the vampire is physically and emotionally frozen in time, which would mean the soon-to-be werewolf would not mature enough to trigger the change.
So, IMO, no werepyres.

I think it is possible for there to be a werepyre, but I don't think a vampire would waste its venom.