Go to Booty Bay with one. I think it happens in duskwood also, possibly goldshire as someone posted earlier. The pets will just sit there. They will not follow or attack. It seems to be related to the same zones where the mobs don't do anything. Aggro one and they move two steps and stop. You can only attack them with ranged, magic, or by standing melee in the position where you first aggro'ed them. You can then fight them without them fighting back. When they die, their body goes back to where you aggro'ed them. It's like they never really moved...

I haven't tested every zone but it only seems to be some early level ones. I had a bunch of people on my server as level 40 or lower in the center of duskwood killing the dragon boss and other elite mobs easily. Not to mention farming the elite's outside ZG..