… no they don’t. There are multiple species of what a non-taxonomist would refer to as birch trees. The silver birch tree (betula pendula) is the national tree of Finland and is native to most of Europe and Asia. It’s considered invasive in some parts of North America.

The white birch (betula papyrifera) or the gray birch (betula populifolia) would be two of the species found in North America, and they do grow in the United Stares, not just in Canada.

I had a birch tree on my property growing up in Long Island, New York. I mean it's not terribly far from canada, but it wasn't upstate either, they have a range down into the US as well