I don't remember hearing that on dw20's forgecraft vids, though he did mention something similar in the newest ssp vid at 8:25. He made a cleaver and said that you could drop a mob's hp with a different sword and then switch to the cleaver because "it's the finishing blow that counts."I think it's the bow, as AFAIK looting is based on the item that you are holding when the mob dies, so in theory you could swap from your bow to your looting sword while the arrow is in the air. I think someone mentioned this on a recent ForgeCraft video. I'm not 100% sure of this information though.
EDIT:
Also, still not sure cause Minecraft wiki says "applies not only to kills with the sword, but to any kills while holding the sword" about looting.