Only partially true.

UA has flights which run ORD-HKG-SIN and SFO-NRT-SIN (and many others) which continue onward with the same flight number AND the same aircraft.

NW also has a PDX-NRT-SIN flight which retains its flight number and aircraft for the whole trip. Probably several other flights as well.

However, on domestic legs of these international flights, the aircraft gets switched (I believe the UA ORD-HKG-SIN flight originates in PHL, but the PHL-ORD leg is operated with a different aircraft).

But on international flights which continue onward using 5th freedom rights, it's usually almost always the same aircraft if the flight number does not change.