I think the confusion (and I'm really a beginner so I could be wrong here) is what we're calling the bits. I believe a flush trim bit always has the bearing on the bottom and a template bit always has the bearing on the top.
I could be wrong, too (a beginner woodworker also), but the link I provided (
http://www.freud-tools.com/freudtopbear.html ) says "Top Bearing Flush Trim Router Bits", instead of template bits. *shrug*
My guess is
most flush trim bits are bottom bearing, while some are top bearing. And then the names are treated sort of like rectangles and squares; while squares are a special type of rectangles, the false statement, "that's not a rectangle, that's a square" is often accepted, as well as the corollary "rectangles are not squares". ("Mouse" & "trackball" is another place this happens.)
BTW, misunderstandings due to "most means all" like the squares/rectangles one can be fatal. Example: there are two different types of strokes, clogged vs bleeding (not the real medical names). Most are of the clogged type, so "stroke" often incorrectly means the clogged type only. Such as "asprin a day helps prevent strokes" and "asprin can help stop a stroke". While true for preventing the clogged types, asprin can impede a bleeding type stroke from stopping the bleeding, thus extending the stroke.
All people with friends or relatives with aneurysms or AVMs be aware of this, as strokes on people with aneurysms & AVMs
usually, but not always, are the bleeding type, but other people can have brain hemorrhages too.
Sorry for the OT.