There are three different logs that show that same thing. If I pot while the shot is in flight it doesn't gain the buff. If I fire just as the buff is falling off the buff wears off before the shot hits the target but the shot still have the buff. I could be reading the logs wrong or there could be some funky thing happening with lag but as far as I can tell BA snapshots when cast and not upon hit. I also did a log for serpent sting. When doing that ability the only thing that decided if the DoT was buffed was if I had Vermin's Bite when the DoT was applied to the target.
http://i.imgur.com/y3FHGNw.png Best I could do for a direct source we can all trust 99.8% of the time (been discussed before and someone tested it. Pretty sure it was MMO-C hunter forums you can dig into), point is that that all DoTs/debuffs/stuff the player applies to the target as a debuff snapshots on hit. It's like this with all dots in the game iirc - the fact that it applies for Serpent Sting should be a decent enough source, though. (That's from the EJ BM guide so it didn't list Black Arrow, checked SV one but it's not nearly as well done).
If you've been around for any decent amount of time you'd kind of have read threads about it, though. Not trying to be a jerk either but naked character or not, Blood Fury is a pretty weak cooldown to use it with.
As for knowing it, it's not really a big deal.. Like at all, I can't think of many cases where this knowledge is really relevant and the few cases I can come up with are RPPM-based randomness.
So yeah, "common knowledge", you linked a BM theorycrafting guide that has no mention of BA at all and just assumed it did the same thing as the other ones listed.
I don't blame you since it makes logical sense but Aldarana and I's testing proves otherwise.