First, Constantine can not buy in Greece because he has no legal personality, it is due to 1994 law, it is on the official website, and he mentioned this law in the ABC newspaper.
Protothema was the newspaper that said that Constantine was building a "new Tatoi" near Porto Heli, and other newspapers claimed he was moving to his new house ... but he was not building anything, it was not true,( I remember on the official website there was a statement asking that the news were rectified, ).
The Kings of Greece live part of the year in Britain Hotel , Athens, on zone dedicated to apartments(he explained about it in ABC newspaper in june) and he said that in Porto Heli he lives in rented house . In 2003-2013 they lived in a house in Porto Heli, it was very open to the sea, but when they decided to settle permanently in Greece, they moved to another rented house in Porto Heli by motives of security, this home is inaccessible to the press
I do not think the news is true, because they were moved to one house more safe, and this house as you can see in the picture, has a road from which you can see the pool , garden and the whole house,
I think that it is like the NEw Tatoi of Protothema,
I remember that the press was saying that Constantine and Ana Maria lived in their new house, recently built, but New Tatoi not exist.
http://4.bp.blogspot.com/-8JXSu5JldJU/U7rBdCSPQ3I/AAAAAAAADP0/zLPzkA_DqUk/s1600/portada+del+abc.jpeg
interview in ABC newspaper.
Constantino de Grecia: «Una república no resolvería los problemas de los españoles» - ABC.es
in September, they gave an interview to the Danish press, Billed Bladet, in their house of Porto Heli, they did not spoke to change of house,
https://pbs.twimg.com/media/ByT0d0gCEAMsBwP.jpg
https://pbs.twimg.com/media/ByT0eWZCcAACQEE.jpg