What evidence is there that the Navajo and Apache tribes share a common ancestry?

The languages spoken by the different Apache groups are all clearly very close to the language of the Navajo. All their languages are classed as Southern Athapaskan and it can be shown that these tribes all originated long ago in the northern part of North America, where the "parent" Athapaskan languages still remain today.

Some examples: Navajo for bone: ts'in, Western Apache: ts'in, in Mescalero Apache: ts'ine.

Water: tó in Navajo, tóo in Western Apache (falling tone longer o) and tú in Mescalero.

Attached is a short video by a Navajo speaker comparing the two.

There is also genetic evidence linking Athabascan speakers.