It just depends on the NA's you're talking to. We're all different. Some NA's do have an attitude when it comes to people saying that GGGG grandma was Cherokee mainly because the Cherokee integrated much sooner than a lot of the other tribes, and in their minds the blood has been diluted a lot. This doesn't make their attitude right, and I certainly don't share it, but that's their reasoning.
I have both types on both sides of my family. Some of my Lakota relatives have certain attitudes such that they believe that if you are not an enrolled member of a federally recognized tribe, then you are white. That's it. They don't care if you are as brown as you can be, with coal black hair and black eyes, and can show them on paper that your grandma was a full-blood. You don't have that piece of paper from the tribe saying you've got a number, you don't exist as an NA to them. It's sad, but that's just the way some are.
Then there are people like my husband and his Nez Perce relatives who believe that it's what you identify with that matters. So, if you identify with being NA and you go to powwows and other cultural events and you "hang" with other NA's, and that's what you feel you are, then that's all that matters. It just depends.
I wouldn't let one experience with a few NA's cloud your perception of NA's as a whole. You also need to take into account that these dancers didn't know you. You can't expect NA's to just hand over information to you that they may consider to be sacred just because someone says they're NA. You have to hang with them for a while and get to know them, once they see that you're serious and sincere most likely you'll get the answers you are looking for, providing it's not something that isn't discussed. There are some things that we don't talk about because of their spiritual nature, but if you are around enough, and sincere, you will eventually learn these things by observation.
If you're identification is NA, then that is something to be proud of. :-)