In the case of the technique used here, Factor Analysis, there's a lot of user input/judgement required, which is probably why the authors saidDifferent groups could have taken the same data and come up with 4 or 6 factors, and they could all be right, ie it's a matter of opinion - to some extent (with 4, 5 or 6 factor solutions, 4 of the factors would be very similar across all solutions). For that reason, Factor Analysis findings shouldn't be seen as absolute.
It's notable that the authors 'Inflammation' factor included both sharp chest pains and dizziness, neither of which is obviously linked to inflammation (and neither of which is part of Fukuda), which helps to illustrate how the factors are not exactly absolute.