"Supplying voltage via the 5V or 3.3V pins [...]" to what?

Paul__B:

CrossRoads:
If external power is supplied to the 5V header pin while the barrel jack is unpowered, the 5V regulator can be reverse driven & damaged. To avoid damage, connect a diode from 5V (anode ) to Vin (cathode).

That makes no sense.

For a start, the USB port does precisely that - supplies power to the 5V header pin and thereby the output of the regulator.

Yes it makes perfect sense - regulators are susceptible to damage
if reverse driven, since this reverse biases the pass transistor EB junction
(the easiest way to blow a transistor). Individual regulators have idiosyncrasies
too, especially LDO ones.

The Uno and Mega have power-switching circuits that detect Vin
and switch over to USB only if Vin is low.