The title of the post is taken directly from the "Eight Points of Jurisdiction" manifesto of the Haudenosaunee Confederacy Chiefs Council written in the HDI Wikipedia page. See here.
Crown jurisdiction over the matter no longer exists in any direct manner. Despite various Six Nations groups approaching the authorities in Great Britain (the Crown), the latter always state that the aggrieved party will have to approach the party whose responsibility it is to administer the former duties of the Crown, and that would be the Federal Government of Canada, and more specifically, the Minister of Aboriginal Affairs and Northern Development". The wording of the Indian Act is very confusing at best. For example:
18. (1) Subject to this Act, reserves are held by Her Majesty for the use and benefit of the respective bands ....
Since Canada is a Constitutional Monarchy, it is understandable to see "Her Majesty" mentioned in legal documents but the defacto relationship between parties is as noted above (confusing, yes).
Also, the "We require" is of course a demand. It is generally a good idea that a demand be made only in a very restricted range of circumstances, such as when something really drastic has just recently occurred. For example, changing the Indian Act (which was last revised in 2013) which say changes the ability of Bands to governs their own membership lists. However as a blanket way of dealing with Government - not a good idea.
In the general population if one wants an investigation of a matter than extends back to the era when the British Crown did hold sway over "Indian Affairs", then does it seem reasonable to "require" that the taxpayers of Canada pay for what might be (say due to the condition of the records) a very long and arduous process. Considering the rather large sums of taxpayers dollars that flow into Six Nations coffers each and every year, Band researchers may best be able to use some of these resources (or those from for example the HDI) to obtain details from the records, have a report submitted, then if the Federal Government disagrees with the work, they would then need to conduct their own enquiry. Would it not make sense that the two research teams collaborate, especially since in the past the Six Nations have refused to acknowledge the conclusions of the Government researchers and their legal advisers. Since, as has already been noted, some collections of records have been removed to the Band Research Office, the Government may be embarking upon a project with one hand tied behind their back - and when records are incomplete, no one ends up being satisfied with the findings, potentially being riddled with holes.
If the matter is recent, then sending in ones own auditors would make good sense - they could flag any discrepancies. However, do the Six Nations really trust the Government to do the work for them?
Of course the exercise may open up a can of worms that will occasionally work to the disadvantage of the Six Nations. What if multi-millions of dollars of taxpayer money had been dispersed, but upon detailed enquiry, there is found to be no legal reason why these funds had been released? Would the taxpayers be reimbursed?
This could be a knotty or thorny problem, and there are times when one should be careful what one wishes for - it all may come back to bite you.
Perhaps the statement, one of the "eight points" is meant to refer to matters of long ago, where normally the statute of limitations would apply. However it seems that some in some matters "everyone" has come to believe that the Six Nations were cheating in this or that situation, and that compensation is due. What comes to mind as a classic case is the funds invested circa 1837 in the Grand River Navigation Company. Is this what the Chiefs have in mind?