That stat is probably only true if you look at things in a certain way -- for example, a highly restrictive definition of "linen". Pretty much every source I've seen says that the top five producers of linen fabrics are China, Italy, Ireland, Belgium and the USA -- with China dominating by far.
That makes sense. Reading a bit more about it, it seems that currently, 80% of the French (raw) linen production goes to China to become fabric (sorry I'm missing some vocabulary here) :/
That's interesting, why is it so concentrated? Is it subsidized heavily?