You said it, not me. You have already admitted that you do not dive a BP/W, you dive a back inflate. That covers the limited experience. Your understanding of physics has yet to be proven as well. For it to push you, it has to have more air than necessary to stay afloat. Those of us that do dive BP's will agree with Peter, in that it depends.
I will take issue with that.. I have back inflate, SS back plates and Aluminum back plates... and dive with a lot of different tanks and with a lot of different exposure protection.
My regular BP/W setup (HP steel tank, 5mm suit) is a joy underwater and on the surface... I can inflate it till air comes out the over pressure valves and I am upright. But take that same rig, and put an aluminum tank in it, and I have to be very careful where the weight is and how inflated it is, or I get a face plant. Put 4 lbs of weight on one of the tank straps and the problem goes away.
However, I borrowed a 63 cubic ft tank for a shore dive, and to my surprise, it actually wanted me face down in the water. I found it surprising difficult to get upright, even leaning back did not work. I assume that If I had moved all the weight to the back, I would not have had an issue, but was sure not expecting it to be that bad.
I have also seen and used LP steel tanks where you end up leaning back on the surface (which is not fun in big waves).
Rather than say it doesn't happen, it would be better to say it is something one should be aware of, and move weights around as needed to correct it.
It should be obvious to anyone that putting all your lift in back, and then using a buoyant tank, that it's natural position would be leaning forward.
It can be an issue, it is usually correctable and it should not be a reason to buy or not buy a BP/W