Are you referring to the Sullivan of this profile being removed from the Nazatico Project? Yes, we have your kit and have ferreted out the Fugate/Martin and we absolutely know the Sullivans of Ireland married into this group. Since it is oral history, geni being a rule driven data base, only allows paper trail and sometimes allows atDna when done with ISOGG standard work, which this line was. Thanks for your comment.
I am a direct male line descendant of John Thomas O'sullivan (Sullivant). I have also been hearing a similar story for much of my childhood however, it is somewhat different, in that, it is an "in-law" relationship through Nanzattico Talbot and John Talbot.
There is no direct blood relationship that I have ever been able to find. My understanding is that the Sullivan line's Native American heritage by blood is largely Cherokee (through Sequoyah) and Choctaw, possibly some Muscogee.