My understanding is that the Queens cousins who live in KP do pay a "peppercorn" rent which is a very small amount each year a couple of thousands). Prince and princess Michael are slightly different as he is not in the line of succession (at present anyway) and does not officially represent the Queen on a day to day basis. Thus the argument came about from the parliaments accounts committee that they were living rent free and unlike the other royals not working for the Queen in lieu of rent. The Queen paid their rent for several years as she felt she had promised them an apartment in the palace, I think in the mind of the Queen and her staff the couple would move to their country house, instead they sold the house in the country and made the palace their main home, as such they had to start paying rent at a more commercial rate.
IMO this should be the rule, those who don't work full time as a royal should pay rent, by this I mean for example, the York princesses, they do not carry out duties listed in the court circular and have their own jobs so should pay rent for the st James' palace apartment, I think the same should have been done when Edward and Sophie were working, they should of paid rent even if they were still in rooms at BP. I think it's fair enough for those full time royals to get a place to stay as that's where their staff and the royal court are based but any others should pay rent.
In the case of Beatrice and eugenie I imagine it was 'justified' on the grounds of security.