Pin 14 on a Mega is an actual Digital Pin and is not the same as Pin 14 on the Uno (which is an Analog Pin).
That statement is misleading.
Pin 14 on a Mega is a strictly a Digital Pin and is exactly the same as Pin 14 on the Uno except that on a UNO, pin 14 is also is an Analog Pin.
I think that when you accept that, your "problem" will go away.