American Gypsies is a reality show put on tv to get ratings, so like any other one it is going to be exaggerated and play to what the public wants to see. However, it still gives some of the basics of Roma life here in the United States, knowledge which we didn't really have before.
As we know American Gypsies is all about American dream and their own rule and own power, but a Roma society shows what every one has in common. As a matter of fact these two subjects are as appose to each other because one of them more talks about commonality and the other one talks about own rule and a unique version of power.
I don't think any TV show depicts the right aspects of any culture correctly. The issues that are faced with, what is real and what isn't, are too large.The Jersey Shore is a good example of this, and I doubt Duck Dynasty people are really like that as well. The Osbornes are not as crazy as you think, as well. The whole reality TVthing is some real blended with a lot of fake.
"American Gypsies" does not accurately represent Roma society. Roma are European gypsies mainly. The family on the show is also very successful. The Roma mainly are drifters and do not maintain established lives like they might do in America if they choose to assimilate. This portrayal is incorrect for an overall view of gypsies.
Reality shows, like the rest of television programming is for entertainment. We pick out the biggest train wrecks or the most successful people to get more viewers. Just like the "Jersey Shore" didn't embody all New Jersey/New York residents, "American Gypsies" does not show the average personality/behavior of Roma society.