Has that in fact happened?
> we've lost their trust & aren't entitled to the pieces of the puzzle they may have
That would be unfortunate, but if you're an anthropologist who'd like to solve the puzzle, what should you do?
Certainly. I've heard of some native archaeologists, but I'll confess I'm not super up on the topic.
> If you're an anthropologist who'd like to solve the puzzle, what should you do?
Well, if you're an anthropologist, and some group of people makes it very clear they aren't a puzzle & won't be studied (say, the people of Sentinel Island) - go do something else maybe? Curiosity doesn't entitle you to answers, there's plenty of other stuff for an anthropologist to do. I feel like the first rule of anthropology is, "respect the culture you're studying and take it seriously," and if what they're telling you is "mind your business" - well, listen.
Returning to Sentinel Island, we might not know why they don't want to talk to us, but they've made it abundantly clear that the lines of communication are closed. Surely we could spy on them from satellites, drop surveillance devices from helicopters, et cetera, and start to understand their culture that way. For that matter, we could create some sort of arrow-proof vehicle and overpower their efforts to repel us. But why should be? Just because we're curious about them? Why should we privilege our curiosity over their clear desire to be left alone?
And if they are interested in sharing their oral tradition with you, and you sneer at it - well, they might rescind your invitation.
In any case, what constitutes "sneering" at their oral tradition? As you said, science & religion are not the same. So what should a scientist do if their beliefs differ from science's?
Sneering would be something like saying, and I mean this with all due respect, "you didn't come out of the ground in that canyon, we all came from Africa" - misconstruing what they're saying, seeking to correct rather than understand, generally being rude and dismissive. If someone shares something with you, it's up to you to figure out how and whether to incorporate it into your epistemology; if you're having trouble with that, it might be tempting to say, "the problem is that your epistemology sucks," but a.) That's an indecent way to treat someone and b.) No one is going to learn anything that way and c.) The problem is actually that you gave up on trying to understand, not that there was no resolution to the conundrum, and not that their epistemology is "inferior" in some way.
Consider that when a native culture has an origin story involving a specific place, regardless of whether we have believe that humanity evolved there, there is really no reason to doubt their culture emerged there and that that place has an important bearing in their.
I'm pretty sure that's what I would do.
So how would they be left IN? Would the archeological community say to them, respectfully, "Our evidence is that First Peoples arrived from Siberia somewhere between 20,000 - 10,000 BCE. What do you think?"
So what would their reaction be? Would it be:
1) We don't know; our myths don't go back that far; you tell US, or
2) You are a colonialist to even talk about this.
??