Does place of birth have meaning?

[Cannon]

So according to this, even though I am American but was born in Greece, would I still be American on the next incarnation, regardless of place of birth?

According to my understanding informed by the Ra Material and what some people claim after having near death experiences, your next incarnation will take place anywhere (or when) you damn well please, provided someone is capable of giving birth to you. The Ra Material says specifically that once a soul reaches a certain level of development in third density, they can choose whatever they like, to the point of their own detriment in some situations (such as if they ignore advice and decide to have lives in which the lessons are too intense for them to handle at the time.)