The website certainly provides a lot of interesting information, but I'm not sure it really explains (in terms that are simple enough for my liking) why the vehicle must be inverted during its ascent.
My hypothesis goes something like this:
I think I am correct in saying that the orbiter is fixed to the fuel tank such that its nose is closer to the tank than its tail. This means that the required slightly negative (zero lift) angle of attack could be achieved without inverting the orbiter.
The solid rocket boosters are fixed to the tank, so their thrust line is probably fairly close to the drag (and inertia) line of the tank. This, together with the thrust from the main engines , will produce very little pitching moment during the initial stages of the launch.
But once the solid boosters have been used up and all thrust is being provided by the main engines, the misalignment of the drag+inertia and thrust lines will produce a large pitch down moment (towards the tank). If the inital thrust line of the main engines was parallel to its longitudinal axis, this would require a good deal of thrust vectoring to trim the vehicle (I assume they do not use ailerons at this stage). This continuous thrust vectoring would reduce the overall performance of the vehicle.
The alignment of the exhaust nozzles suggests that the thrust line of the main engines is not aligned with the longitudinal axis of the orbiter, but is angled slightly towards the front of the tank. By inverting the vehicle the drag+inertia lines of the tank and orbiter become better aligned with the thrust lines, and (when ascending inverted) with the intended direction of flight. This helps to trim out the pitching moments whilst maintaining performance.
This is of course only conjecture and was in fact (initially) constructed in the scenario you described in your previous post (in a pub over a pint).