Precedence for Britain's Princess Michael of Kent?

Some years ago Sarah, duchess of York and her daughters Princesses Beatrice and Eugenie boarded a plane and were seated in the first-cl section. By coincidence Princess Michael of Kent boarded the same plane and wanted the seats that were occupied by Sarah and her two daughters, claiming that she (Princess Michael) socially outranked Princesses Beatrice and Eugenie. The airline personnel consulted Debrett’s Peerage & Baronetage, which confirmed that Princess Michael's claim was correct. Sarah and her two daughters vacated their first-cl seats. How is it possible that Princess Michael--a princess only by marriage--takes precedence over Princesses Beatrice and Eugenie, both princesses by birth?