Today's training is becoming generally more truncated - CBT at home instead of 'chalk and talk' in a classroom setting, for example. I would imagine that some instructors nowadays have forgotten - or never knew - why Port and Starboard are less ambiguous than Left and Right.
No time to check this, but I think 'Starboard' comes from the steering board, fitted on the right of ships, that was used before a central rudder became possible.
Any vessel's orientation is based on it travelling forwards, so not too much chance of confusion. ATC use 'left' and 'right', but of course, pilots seated at the front of an aircraft will be in the correct orientation for those instructions to be unambiguous.
If observing a vessel though, or in accident reports, as the OP points out; 'Port' and 'Starboard' is more precise.