I was a bit quick to say it worked, as I have just found an error.
If you see this category for example: http://fightgear.dk/49-bjj-gi-kimono
On the second row on the right is a product called "Nova Basic Gi, hvid, inkl. hvidt bælte" - it has the grey button (not in stock). But if you click to the product page, it is actually in stock in to variations. I think it's because the default variant (A2) is out of stock.
From the product list, the button "Choose variation" should be there if any of the variants are in stock, regardless of the default variation being out of stock. As long as any variation is in stock, it should display the "Choose variation" button.