I think this must be a matter of status. The Greek Royal Family is related to most royal houses including the British and Constantine II was still a monarch.
The same is true of the Bulgarian Royal Family. King Simeon II was still a monarch.
The same thing happened with the Romanian Royal Family when King Mihai lived. Currently, the Romanian Royal Family still has a semi-official role in their country.
The Serbian Royal Family also has a semi-official role in their country and they still live in their palaces.
It was also these non-reigning royal families who were invited to Queen Elizabeth II's Diamond Jubilee in 2012.
CP Alexander was Elizabeth II's Godchild (as was Theodora of Greece) and HM Margareta was a Goddaughter of Prince Phillip (along with Philippos of Greece), so there is an additional connection to the bloodline. Georg Friedrich and Maria Vladimirovna are both descended from Queen Victoria, so the family relationship to them is closer than it is to Emanuele Filiberto and Archduke Karl.