Infanteer, its the nautical version of "muddy boots".
In the absence of said boots we are at a decided disadvantage when somebody else plants their own boots on the ground. If we are there first with one pair of boots then that forces the other guy to either escalate to a confrontation or go home (or as Kevin suggests remove the boots by subterfuge and hope nobody notices). On the other hand, if the other guy gets there first and can put many boots on the ground our adoption of the "confrontation" option becomes something of a non-starter.
A Major of my acquaintance was reminding me of a Wellington/Napoleon tale. Ownership of a bridge in France was in question. Wellington wanted to keep it standing, other elements (either Allied or Enemy) wanted to have the bridge brought down. Wellington's solution was to park one soldier with musket in the middle of the bridge and keep changing him out every two hours. When it was pointed out that those that wished to bring down the bridge could easily remove one soldier Wellington's response was that it wasn't what one soldier could do. It was what that single red coat represented - an incredibly high political barrier.
In the absence of Canadians working the territory under dispute a government presence is required: Navy, Coast Guard or RCMP launch. Giving the "leap frogging" claim I am going to assume that the waters are too great for the RCMP and the Navy is probably a better bet. Even one Halifax is enough to make the point that we are serious about the claim. That forces the other side to up the ante. A dangerous proposition if we have friends. Less so if we are isolated.
If on the other hand we let the other side plant its own frigate in those waters, and we can't offer more back up than they can, then once again we are reliant on "friends" to establsh our claim. What was a squabble between two "friendly" governments then becomes something much more interesting.
And in all circumstances we lose - face, sovereignty, control, resources.
This is not about penis-measuring. This is about how do you deal with situations that see submarines playing tag for 30 years or Islandic Coast Guard Cutters cutting fishing nets and being shelled by Royal Navy Vessels. Or closer to home its about Captain Canada shelling and boarding Spanish and US fishing vessels.
All of this happened and no "wars" were declared.
EDIT: The Propaganda Wars Begin? Brigitte Bardot tied to the bow of the Charles de Gaulle coming to save the seals from those nasty Canadians. They obviously can't be permitted stewardship over any more of the ocean.
http://www.cbc.ca/cp/world/051205/w120552.html