From Google Maps, it looks like you can drive from Skagway to Whitehorse, whereas to go to Juneau, you’d have to wait for the ferry. Makes it a no-brainer for emergency care.
I would say that the people in Skagway have more of a connection with Whitehorse than they do to Juneau... :-) ... really ...
And Palin knew that, having lived there. And she was talking to those in Canada who knew that, too.
Skagway is rather unusual for Alaska Panhandle towns to have access to Canada via highway.