We have discussed this many times in other threads and it is not as simple as you portray it.
There is a significant sampling error from the Amerindians. The samples are only done to those extant survivor groups, and preclude samples from the hundreds/thousands of groups which had become extinct.
A couple of examples:
The Chicago study showed that a full blood American Indian has a common ancestor with a woman from Greece.
The study on haplogroup X showed differences between the Siberian samples and Amerindians, and concluded that the common group needed to be found elsewhere.
Granted, as you state, I over-simplified my presentation of mtDNA. But your idea that haplogroupX (Ojibway natives) should relate to a woman from Greece was in a study that was premature in its judgement. Recovering mtDNA is not possible from skeletons so you rightly state that the sampling excludes extinct groups. Whether there were hundreds or thousands of such extinct group is also wild speculation. But the library of mtDNA is ever increasing, as are the now millions of artifacts from early populations. So far, the links to Europe are the matter of fringe research that has found little support.
". . . the popular depiction of Kennewick Man as a pre-Columbian Caucasoid in the New World, coupled with the discovery of haplogroup X as a founding Native American lineage, fueled premature speculation about early European migrations to the New World. Genetic evidence does not support such a migration. "
Mitochondrial DNA Studies of Native Americans:
Conceptions and Misconceptions of the
Population Prehistory of the Americas
JASON A. ESHLEMAN, RIPAN S. MALHI, AND DAVID GLENN SMITH