Discussion at Indigenous People's Day

As most of us at MEChA know, this past Monday was Indigenous People's day. In writing this post, I knew I wanted to discuss something about the holiday, but as those of us who attended the lively dinner held by our Native American brothers and sister know, it's difficult to choose between the many issues that surround the topic. However, there was a moment that strikes me as particularly interesting, and it occurred before we even started the discussion.
Not unlike many gatherings at Yale, we began by going around the room and introducing ourselves. The procedure, though necessary, was formulaic as always: name, year, college, and subject of study. But probably because of the nature of the event, everyone found it essential to include what kind of not white minority they were. I have personally never seen such personal, political boldness of this kind at Yale. In a way, we were stating quite clearly that any purely white individual would be either quite unwelcome at the event, or at the very least quite uncomfortable. With our statements of minority identity, we shut the room to all majority members who by simple fact of blood would not understand the nature of Indigenous People's day. (Perhaps this is what gave some of us the courage to speak from especially radical, even anarchist, political stances.)
I don't have any analysis of the ethical implications of this act, namely answering whether or not it was right to exclude in the way that we did, but I'd like to hear what you all think of the matter. Don't white people have the right to advocate too? Or is any kind of aid white people provide a form of "neoliberal" (a term thrown around at the table quite a lot) neocolonialism that only reasserts their superiority? If so, what can they do to address the problems? Perhaps address them within their own infrastructures, within the larger, more deeply ingrained systems that created, or at least exacerbated, these situations of inequality in the first place.