That's Good King Phil, guys.
I'm pretty sure he invited Delphine - possibly nudged by Good Queen Til - because Delphine was very clear in her press conference and other statements that she wasn't expecting anything and wouldn't force herself towards him.
These two are family.
Who in this world would not want to at least meet a hitherto unknown or unofficial sibling, even if the veracity of the connection had to be forced through Justice in a very public manner? Who would ignore, or worse, deny, someone who is half you?
Such a large part of our selves, our characer, is 'pre-programmed' by our genes (much more than you'd expect), by our 'physical heritage'. I bet these two have plenty of similarities, even in movements.
Besides, IIRC Baudouin and Fabiola, childless yet very kind-hearted towards children, played a large role in Phil's life when his parents were otherwise engaged. B&F must have taught him the importance of being kind and forgiving.
After Baudouin died, the throne could have gone straight to Philippe since Albert was already 60 yrs old. In fact, Philippe had been preparing (and was educated) for this role since it was clear that Baudouin and Fabiola would remain childless. Yet, when Baudouin died, Philippe was still unmarried and considered not too bright and rather awkward (so not (yet) king-material), and his dad took what he (as a second son with 60 years of ennui under his belt) deemed his (and which, technically, indeed was his), and ascended the throne (that actually sounds quite GoT-ish) in 1993.
With his dad kinging along, Phil got engaged and married within the span of 3 months in 1999, got four wonderful wafflets (I'm tooootally stanning Liz the Soldier right now), with his very boring, but absolute ace of a wife GQ Til, lost quite a bit of his awkwardness (maybe all he needed was a good shag, right?), and STILL had to wait until 2013 to become king.
Phil turned 60 this spring (yes he did), but is more youthful after 7 years on the job and has so much more energy compared to his dad had at that age (ok Albert has heart problems).
Anyhoo, IMO Delphine is not the calculating nor evil kind, and meeting with her sibling is a very healing experience for her.
Just my 2 eurocents.
Oh and about the house plants: theyre bulbs, namely parrot tulips on the right and fritillaria (we call this variety lapwing flower, kievietsbloem) on the left. The bell-shaped flowers are supposed to hang like that. The flowers may be artificial, but could also be raised early (if you store bulbs cold to pretend it's winter, you can make them bloom any time of the year).
Excellent summation Pommers!
If there was any hope for a monarchy in Belgium it's because of Baudoin and Fabiola raising Albert's acknowledged children as their own. I don't think the Belgian people would have stood for a repeat of Albert II and both he and Paola were too busy wandering the world for their own jollies to worry about the raising of a future monarch. They are both vile people and I gag a little every time I see them acting super pious at some religious event now that they're facing meeting their maker.
Kudos to Phil and Til, and to Delphine for standing her ground. I love the flowers and decor, I would dearly love to see Laeken some day it's such a magical place. This meeting is just what my weary heart needed, God bless everyone involved in bringing it about.