I know this article probably faithfully represents local mythology, it is a badly flawed myth ... either it is just that way, or someone needs to check what they've written and align it properly with some sort of historical reference.  

Assuming that J.C existed (before anyone picks my grammar apart!);
 There is no record in the new testament stating he was born in a stable, that's a misinterpretation, and as far as I know a fairly recent one, based on references to animals and mangers being inside a house.  
 The house in question is in Bethlehem according to two gospels and a prophecy.  
 Although the place of birth is disputed (and, I think, it is generally thought the original gospels had him being born in Nazareth) the passages about Mary and Joseph staying in a house/stable relate to a supposed trip to Bethlehem.  
 Bethlehem is a long way from Nazareth

Either the story should say Bethlehem, or the stone is some sort of crib from a house in Nazareth, or the myth itself is based on an alternative historical version (I was going to say inaccurate, but given we've already got two contradictory and both disputed accounts of possible event it's all a bit of a matter of opinion anyway!)