Cherokee, the specific subject of Elizabeth Warren's claim, weren't like turnips that fell off turnip wagons as the wagons bumped down rutted, dirt roads. They weren't like seeds that randomly sprouted up all over the place with no other connections.
Cherokee, whether eligible for enrollment or not, had family. Parents, siblings of parents (aunts and uncles), grandparents, their own siblings, spouse(s), and children. No Cherokee operated in a vacuum all by themselves. The names of relatives can be found alongside "white" members in Cherokee records, often going back 3 - 4 generations: the Dawes Final Roll, which is specific to Oklahoma between about 1890 and 1906 - and the Guion Miller Roll, in particular, is a great wealth of information for both Cherokee and the thousands of non-Cherokee (whites) who also tried to get a piece of the monies owed the Cherokee who gave up their lands in the East.
For all the claims of "hiding out", "fell off the Trail (of Tears)", "married a white wo/man", "hid in a cave", or "was ashamed" etc., there will still be documentation. Of the hundreds (thousands?) helped, not once has any of those claims (excuses) been proven. What has been proven is that all ancestors, going back well over a century of time (from the very early 1800s up through to 1940) have been found on US Federal censuses. They've been found, nicely documented, when no Tribe or its people were considered to be part of the United States (as in "citizens").
