This has been a topic of discussion among the belly dance world since I've been around. So I'm willing to bet it's been much longer since the discussion started.
It's hard, even when speaking with someone FROM the country of origin to really nail down what's correct in their dances. But usually, in my experience, a very close approximation will make natives of the culture happy. I think it's the dancer ultimately who is hardest when authenticity comes into play.
It seems a dance performed by a non-native is scrutinized moreso on the basis of the feeling of the dance. Sure, the movements need to be right, the costuming has to be close enough to be recognizeable, but the feeling or tone with which it is performed speaks out louder than those things.
There are couple of concepts in Central Asian dance that address this. And no, I am not a scholar in this subject so I may be a bit off.
One of these feelings is known as kaif. Kaif is a sense that closely resembles exctasy or perhaps it would be better described as a peacfeul exctasy. It's not an overflowing, in your face, hippie at woodstock kind of emotion, but it can be much more impactful.

You can see kaif in this video of a Uygher dancer. She isn't doing much for awhile there, but you might be able to see what I'm talking about: www.youtube.com/watch

Another such emotion is known as noz. Central Asian dances come from primarily muslim societies where women who dance out in public in the first place are frowned upon. But those who do dance reflect a subtle expression of emotion expected of women. NOZ is a very subtle coquettishness that may go un-noticed by people from a more brazen culture. I can't find a good video fo it, but it can often be characterized by looking at the audience out of the corner of the eye rather than in the eye and by use of hiding behind the hands. There are een movements that mimic hiding behind and peeking out from under the veil.