As I understand it, the original name was Ammo-Oil after Al Amatuzio's military nickname "Ammo". Apparently Amoco objected to this, so the name was changed to Amzoil. Pennzoil then objected and the name was changed to Amsoil. Then Amway objected, but Al won that suit.
Since the early fame was made on the Amzoil name, the correct pronunciation has the "zoil" sound.
Tom NJ