The article linked states "U.S. believes the passage to be international waters." That is untrue; the US believes it to be an International Straight under UNCLOS, as does China. There are areas where it cannot be International Waters because it is less than 24nm wide, therefore it is de facto Canadian Sovereign Waters.
The US position is actually "The Northwest Passage is a straight used for international navigation. Therein, all ships and aircraft enjoy the right of transit passage, in accordance with international law as reflected in the 1982 Law of the Sea Convention. The enjoyment of transit passage is not subject to prior notice to, or permission from, Canada as the State bordering the straight."
http://www.state.gov/documents/organization/98836.pdf
Further, from the President (Bush): "we believe it's an international passage... We'll manage the differences, because there are differences on the Northwest Passage."
http://www.nationalpost.com/news/story.html?id=57868baf-87b0-4f29-9a4f-b6251b48582d&k=92663
As well, economic control over the entire straight (fisheries, oil, etc) is Canada's as it is part of our 200nm EEZ.
The issue isn't that someone is going to suddenly decide to go up there and take it; it's whether or not Canada wants to maintain (exert?) exclusive control over who goes through it. What is and isn't an International Straight is governed by customary law: if it's always been that way, then that's the way it is. However, this is a point of disagreement because those who believe it is an international straight think that the only reason it hasn't been used continuously as such is because it couldn't be (due to it was frozen).
When (and if, although I believe when) it can be used as a straight, then if countries start to use it as such (companies can't, as vessels are flagged by states), and we don't challenge it, then it will in fact become an international straight. Strongly worded letters will mean nothing.
This why we need the Coast Guard (this is there job, not DNDs) to have a permanent presence (VTS, radar, AIS, SAR, air recce, and surface inspection) at the main areas where it narrows. If you don't have permission, and don't subject yourself to Canadian territorial law, then you don't enter. I am not certain the current government cares enough to do that... I'm not even certain the last one did, to tell you the truth (proof is in action, and they didn't do anything).
As the EEZ thaws we also need the ability to exert our monitoring over it.
The only reason we need an armed (ie DND) capability is if we truly believe there is/are nation(s) willing to press the point with an armed escort. I don't think there are; the international response would immediately put them on the wrong side of the discussion.
Now the nuance: Canada also claims straight baselines over the entire thing as an archipelago; ie we would seal the west end and the east end and *all* of it is internal waters. This is more of a stretch since the archipelago section of UNCLOS is more directed at states that consist of nothing but islands. There is much less international support for this; the US certainly has made it plain that if they never enter Canadian 12nm waters they can do whatever they want (from the letter above: "For the record, the United States sees no basis in international law to support Canada's drawing of straight baselines around its Arctic Islands and its claim that all the waters among the Canadian Arctic Islands, including the Northwest Passage, are internal waters of Canada").
Canada's claim is much weaker here. If we intend for that to be our position, then we better start treating them like internal waters and get a robust patrol capability over and on them *all the time*. I don't think we are going to do that, and so by customary use they will de facto become international water's (outside of our 12nm limit, of course). This will in no way change that if the water's are in fact enclosed by overlapping 12nm limits then they are, in every sense of the word, territorial waters.
I wish that commentators on this would actually use the right terms and explain the positions correctly (which Time.com didn't)... but the people that write this stuff see no need to actually give the facts a lot of the time.