As far as I knew, the Minnesota/Mat-Su Valley connection was considered the explanation.
She definitely downplays it in some scenarios (like those older clips) and I think she plays it up in others, probably increasingly as it became part of her "brand".
In this clip, she recognizably has the same accent, but is suppressing it somewhat/not exaggerating it. I
would say that this particular audience would be one that would benefit from her playing up her local accent, except her local accent is not the majority accent in Alaska, so it probably carries little advantage outside of her home area.
There seems to be some disagreement among people who some experience there, but if both Bill Labov and that dialect map you linked to see an Inland North (Minnesota) connection in the Mat-Su Valley, along with at least some anecdotal evidence for it, I'm willing to believe that's the explanation.