I don't necessarily agree with that convention. That's pretty restricting on what makes intuitive sense.
For this particular problem, the way I see it is that if persons A B C and D made the team, then this would be equivalent to saying persons D C B and A made it. There isn't a ranking or hierarchy system here or something, there's just one single team with four members. This implies that repetition of cases does exist, and that I do need to divide by the factorial here.
If, for example, I had to choose positions specifically (e.g. center, forward), then I would not divide by 4!.
The important thing to realise is that division by the factorial is for an unordered selection, which is what we have here. If we have an ordered selection, then we should definitely not divide.