Well, that makes things even more weird, because the product range in my site IS selected in the Root Category (being Default Category). All products are assigned to each section of the category it resides in (so Default Category -> Top Category -> Sub Category are all assigned to Product A as it resides in Sub Category).
The "filter by root" option does exactly that, filters by your root category, for that store. It's used when you have more than one store running from the same Magento installation, but have different products on each and don't want them mixing. So you set separate root categories for each. With the setting enabled they won't be visible to the other store.
So, if you enable it and you don't have all your products selected directly in the root, they won't appear.
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In the above screenshot they're not selected in the root, so you see the 0 next to it. That's what FeaturedProducts also sees, 0 products.
Hope that clears things up for you.