But why would this increase the population of the Spanish ones? Seems like more contact with Europeans would cause the epidemics to spread faster among the Spanish colonies.
Ah yes, the ubiquitous Cherokee great-great-great-great grandmother
Maybe I'm being too harsh, but these wannabes would be more credible if they claimed to descend from a tribe that was less isolated and, you know, actually living near the areas their ancestors lived.
And of course in the Caribbean, the Spanish did pretty much wipe out the native peoples, which to me makes the arguments about different population levels/levels of social organization* seem pretty valid.
*Not as in "hurrah, progress and civilization!", but as in "people who are used to taking orders from central authority get kept around by the new central authority".