A: First of all, let me say that just because a coach coaches something doesn’t mean it falls within the spirit and intent of the rules. As an example, I watched a coach coach her kids to fake contact to get a charge call, which, of course, doesn’t fall within the rules and is now covered by a “faking a foul” signal and warning to the coach by the officials.
So, in pulling in your questions, I’ve included the FIBA Rulebook references that support the fact that what you describe is a foul (references in bold):
33.15 Pushing
Pushing is illegal personal contact with any part of the body where a player forcibly moves or attempts to move an opponent with or without the ball.
47.3 When deciding on a personal contact or violation, the officials shall, in each instance, have regard to and weigh up the following fundamental principles: • The spirit and intent of the rules and the need to uphold the integrity of the game. • Consistency in application of the concept of 'advantage/disadvantage'. The officials should not seek to interrupt the flow of the game unnecessarily in order to penalize incidental personal contact which does not give the player responsible an advantage nor place his opponent at a disadvantage.
In summary, what you describe is a pushing foul as the player “boxing out” is gaining an advantage by displacing their opponent while putting themselves in a better position to rebound the ball. The head coach of the league you refer to is not correct in saying that “you can’t take more than a step or two back once you’ve gotten position” because in actual fact, you can’t displace your opponent at all. So, in boxing out, it’s okay to find your opponent with your hand/body but you cannot push back at all or a foul may be called. So, the player boxing out may hold their ground but can’t push back by either moving their feet or shooting their butt out as both would displace their opponent illegally.