Well that is the biggest load of gobbledegook I’ve ever read. The truth is that practically it makes no difference whether you use vog or vtw except at very low wind speeds and in strong tidal streams. If all that is available is vtw then you may as well use it to calculate true wind because there is usually only a small error but to be mathematically correct you should use vog.
Imagine you a moored to a buoy in a strong tidal stream. The tide is 3 knots and there is no wind. If you switch on your instruments the log will show 3 knots through the water and the wind speed will show as 0 because there is no wind and you are not moving through the stationary air. If you loose the mooring you will drift downstream at an ever increasing speed until you are carried by the tide at 3 knots over the ground. Your log will show no speed through the water but your wind instrument will show 3 knots because you are moving through the air at 3 knots.
But it makes no real difference which speed you use.