Mobs killed by dogs give wrong loot tables

The bug

Mobs killed by player owned dogs don't give uncommon or rare loot. This bug first appeared when loot tables were changed in 15w43 (works as intended in 15w42) and has not been fixed yet. If the dog does the killing hit it will not give uncommon or rare loot.

What we would expect

A player owned dog assist in the player's mob kill by doing the last blow of damage to the mob and the mob's loot has a chance of dropping an uncommon or rare item.

What happens

A player owned dog assist in the player's mob kill by doing the last blow of damage to the mob and the mob's loot has no chance, what so ever, of dropping an uncommon or rare item.

How to reproduce

1. Summon player owned dog:

   /summon wolf ~ ~ ~ {Owner:"UserName"}
   

2. Summon in a blaze:

   /summon blaze ~ ~ ~ {Health:2}
   

3. Punch the blaze once and let your dog finish killing it
4. Repeat until satisfied
5. Notice that the blaze never drops a blaze rod as a loot

It affects all types of mobs (but normal skeletons).

Code analysis

Code analysis and fix by Xcom can be found in fix.png.