Interesting article, which made me go to the Akwesasne website to look up how the Jay Treaty fits into this. It is definitely worth a read, at http://www.akwesasne.ca/jaytreaty.html

Aboriginal Border Crossing Rights and the
Jay Treaty of 1794 Prepared by the Aboriginal Rights and Research Office
Mohawk Council of Akwesasne
Kentenhko:wa / November 19, 1999
Based on the legal history in that article, it seems clear to me that the 1956 decision was non-sensical, because either Canada, as the inheritor of British policy towards First Nations people in the Americas, must now be considered one of the"Countries of the Two Parties on the Continent of America", or else it has no right of jurisdiction at all over First Nations affected by the treaty.
But, by the same token, the very recognition under the Jay Treaty of Aboriginal Rights (or re-affirmation if you will) seems also to be conditional upon, or at least co-existent with, recognition that the border between the Two Parties does not run around Akwesasne, but right through its middle. And that strikes me as direct recognition that Akwesasne is not a sovereign nation (and not one conquered) but one that has voluntarily relinquished its sovereignty, except in certain particulars that we now call Aboriginal Rights, to the USA and Canada. Based on that, it may not be wise to have a border crossing within Akwesasne, but Canada is within its rights to place one there, whatever the sentiments of the inhabitants of Akwesasne. Similarly, inhabitants of Akwesasne may have legitimate moral objections to having armed border guards at that border post, but no legal or treaty case or pre-existing Aboriginal right to oppose them being armed at all.
Now, I am no expert, and may well have misunderstood the nuances of the Jay Treaty and its historical significance and implications today. But, in that case, and I mean this sincerely, I would very much like someone more knowlegeable than me from Akwesasne to explain where I am wrong.