This is something every pan-racial (for lack of a better term) movement will run into. Every movement needs its foundational myths (in the folkloric sense, not the "stories that are false" sense) and common beliefs to function. When you're trying to unite disparate peoples whose main reason for joining together is to increase political/bargaining power, you're going to have to either choose to prioritize certain narratives over others or create new narratives whole cloth. Since legitimacy tends to come from either time or power and these movements lack power, most groups are going to pick the first option (in reality, a mix between the two options). Due to the relative prominence of the Eastern Woodlands in both American/Canadian history and members of tribes from that region in the creation of pan-Indianism, narratives from those tribes are going to be prioritized. And other people are going to go along with it, because joining with the movement is more beneficial than fighting it, especially for something as minor as this.
This reply was actually pretty good:
Fascinating stuff, thanks!