As gravity acts vertically downwards the aircraft decends with the resulting airflow hitting (for want of a better word) the fin area, with the fuselage acting as a lever arm, which in turn yaws the nose into the turn.
Exactly. In other words, it
slips, which in turn causes the yaw -- exactly as BEagle described at the beginning of the thread. And what's more that still happens if you apply back-pressure. You can only avoid the slip by applying rudder, whether it's a level turn or not!