To be certified under Part 23 the aircraft must still be controllable following failure of one primary control system. eg be able to control roll with rudder if ailerons fail, attitude with trim if elevator fails etc.
In testing a type that I fly, they had to test fly with one flap at zero and one at 30% and still be able to control roll with aileron, which the aeroplane easily did or it wouldn't have been certified.
So I call bull**** on the "never put flap down in a turn" theory, unless it is in the limitations section of the POH and I've never seen it there in any of the types I fly.