"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.

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.

Yep. USB power goes directly to the internal 5V rail (and therefore to the output of the 5V regulator NCP1 1 17ST50T3G)