Well, to start, comparing Japan and Canada is like comparing oranges and apples because both of them are fruits. They are both first world countries, but almost totally different in every aspect, even geographically.
You implied that: "If you can get natives to mate with each other, you wouldn't have this problem".
That is not a native or Canada "problem", that is a modern educated civilization "problem". The more educated a population becomes, the less children it will have. Reasons are from economic to lifestyle choices and so on. Having less children or not at all is the reality of a developed nation because they begin to realize the costs, attention, care and needs associated with grooming a healthy child into this world, mentally and physically. Every Western developed country is facing this "problem" if you may call it, but its nature in action here. Studies show that the world population will max at 11.2 Billion in 2100 and then continue to decline from that point on. This increase in population will come from, you "guessed it", underdeveloped nations coming from, you "guessed it again" mostly Africa and parts of Asia.
About the immigration again.
As we in the era of a technology boom, we will need less to do more in the future, almost in every profession imaginable, including doctors and eldery care. The argument that you need a young force to compensate the lost of revenue from the retirees in the future is a short-sighted argument that doesn't take into equation a myramid of factors as from technology, futures wages and lifestyles, business developments and more and more. Not to mention the already producing capacity of Canada for the needed professions.
What you describe right now in BC is a life-changing phenomenon that will self-regulate based on supply and demand. If people want to talk to the doctor through the phone and not visit the clinic, that is what will happen, but if the contrary is in demand, it will be offered by someone/entity/company etc. Supply and demand is everywhere.