Does "Big Stinker" count as "Bad Medicine?"

I'm currently using the "Big Stinker" rune on my Gargantuan:

Big Stinker
The Gargantuan is surrounded by a poison cloud that deals 15% weapon damage as Poison per second to nearby enemies.

I was considering stacking this with Bad Medicine as a passive:

Bad Medicine
Whenever you deal Poison damage to an enemy, their damage is reduced by 20% for 3 seconds.

This seems like it could be useful to make my Gargantuan even more tank-ish. However, I don't know if the poison effect counts as poison damage for the purposes of the passive.

Can anyone confirm (via some repeatable test and/or official statement) that this works or doesn't?

While I was not able to find an official reply from Blizzard, the current opinion is yes: The poison cloud of the Big Stinker rune triggers Bad Medicine.

Several threads exist where people are stating that it works: [1][2][3][4][5][6][7][8][9].