I'm no chemist but I am an engineer, and I do understand several things though I may not be an expert on everything. We all learn something every day. Your explanation sounds complicated for the average Joe Topher. Let me explain it in my terms and you let me know if you agree or not.
I'm not a chemist either, but some would call me an expert in this area or at least professionly knowlegeable. My explanation should be complicated to the average Joe because its an extremely complicated subject. It takes a team of engineers with PhD's to design and develop commercial BMS systems, not your average Joe.
First off, I do understand and know that when you let batteries sit after a drain, the voltage will rise. However, I believe there is a different scenario that causes battery voltage to rise with heat and drop with cold. I don't know the exact chemical explanation for it, but I know about it from my hobbies and have seen it on my Energi. I could leave the car tonight (unplug from charging say at 50% charge and tonight is 40 degrees. Tomorrow the sun comes out and the charge level will be higher, like say 55% for example. I can post specifics later. I have also seen the charge drop from 55% where I left it one day, to 45% the next day when the temp outside was a high of 48 degrees just a couple of days ago. What's your explanation of that (and not counting the relaxation point, that I already know of and agree with).
I think you're having trouble understanding the difference between State of Charge and Voltage. An increase in voltage does not imply an increase of state of charge. The state of charge is merely a measure of how much chemical energy is actually stored in the cell while the voltage is simply the cells electrical potential. The increase of the battery SOC could be attributed to many things like voltage relaxation or Peurkerts Law. I don't know the details of Ford's BMS software so I don't know for sure but 5% error in SOC is very common. Also keep in mind we are referring to open circuit voltage and not voltage under load. Voltage under discharge will increase with temperature due to lower cells internal resistance.
As far as the supercharging that Gary calls it, here is my explanation of that in simple terms. Assume the Li-ion battery voltage range goes from 3.7v dead to 4.2v at 100% full. You never want to exceed those limits and you really shouldn't use up a Li-ion or Lipo pack below 20% capacity or say 3.73v per cell. Anyways, given this, let's assume Ford decided to limit charge to 90% which is I don't know the figure off the top of my head, say for example 4.1v. The system charges the pack until the cells reach 4.1v at which point it stops charging and it shows 100% full but its really 90% as seen in the SGII.
OK, but realistically the voltage range is more likely around 3.3V to 4.1V. An NMC cell is fully charged at 4.2V.
Now if Gary turns on his AC while charging, that draws some power from the system and will drop the cell voltage to 4v (for example, don't get caught up on exact numbers, just illustrating). The AC pulls about 1.5kwh but the high voltage charger pumps in 3.3kwh, so there is more charge going into the battery while the AC is on. The voltage will rise under load of the AC slowly from 4v up to 4.1v, at which point it shuts charging off and says 100% again, but the AC is still ON. Now Gary turns off the AC and unplugs the charger, and the load is gone, and the cells will bounce up to 4.2v per cell and the car will still show 100% but SGII will also now show 99.9% instead of 90%. By using the AC load on the system, Gary has fooled the charging system into thinking the cells are not up to 4.1v yet and it continues to charge more with the load of the AC until it brings the voltage up to 4.1v with the AC running hence you have "supercharged" the pack or in reality just defeated the safety margin than Ford put in to make room for voltage rise when "fully" charged and soaking in the hot sun in Arizona for example. Lipo or Li-ion packs you never really want to store at full charge, best stored at 60% charge or about 3.95v per cell. Anyway, forget about storage charge, that is for long term storage while not in use and usually shipped in this range, but I believe what I explained above here is easy for the average person to understand.
I don't really understand any of what you're saying but Gary clearly stated that he's not charging the battery beyond its charging limits, just simply preconditioning the vehicle. And it doesn't matter if the car is plugged in and the AC is on. The battery is either being charged or discharge, it can't be both, and the BMS will know how much current is going in and out of the battery along with its voltage. And you don't want to store cells at 60% SOC, 30 to 40% is more reasonable. And they are often shipped at around 25 to 35% per UN regulations.