Actually Rat, I hate to be contrarian but there is a small flaw in your arguement. In your initial video you start with your bowline tied improperly. The Tail should end inside the loop. It actually does affect the ssecurity of the knot and in fact when left outside it actually allows the bowline to invert as you warn.
You can see this in the photo from grog ( but you'd find the same in Ashley or any other source)
Then if you imagine cutting your bowline as shown ( Please excuse the crude photoshop) You'll see that the structure of the Sheet Bend and Bowline, forward and backward, up and down, frontside and backside, is identical.
Truly the only difference is one is tied in a single piece of line to form a loop, the the is tied to join two pieces together, especially of different diameter. You can tie a bowline just as you do in your demonstration of the sheetbend, making a bight first and then looping around the other end except when tying a bowline you are usually working with only one end and the standing end is fixed or unreasonably long, but if both ends are free you could follow the exact same mechanics