I see where you come from. The fact that Delphine is a daughter of the Baronesse de Sélys Longchamps does not make her a jonkvrouw as nobility is only transferred via the father. The King has, so far, not legally acknowledged her as his daughter, but I can live with calling her Lady Delphine indeed. The blue blood is there, period.
No idea if this collier is fake or not. What was the reason for this photoshoot? Maybe it was modelling for a jeweller?