I have never ever heard of that. I'll also say that that I've shaved off a ton of edges finished on Thuris and dressed on all kinds of linen without issue.
But, well - whatever works.
I've heard that, here and there on the forums. I tried it and found I like my Thuri edges (and all edges for that matter) best after a good canvas or linen stropping.
YMMV of course.
As far as the linen, I don't really use it at all. I have been using a homemade denim strop for quite some time now. I really only use it for cleaning debris or moisture from the blade. On a new edge, I give it about 5 laps on the denim strop just to be sure there's no grit particles remaining on the razor. I haven't really noticed a whole lot of difference in edge quality either way though.