And that I will accept as fact that powder burning under pressure burns at a faster rate.

Now there is the matter of at which pressures the burning rate increases,and how much it increases.The warning you quoted does not specify this.Does it increase from say atmospheric pressure to say 10000psi,or does it keep on increasing as the pressure increases.Does it increase significantly,or even measurably from say 55000psi to 62,000psi where a 308win operates.That is as of yet unproven.
As to the effect of using magnum primers,primers are a controlled burn rate explosive just like powder,and as such going to a hotter primer has the same effect as adding more powder.I still feel that this is why the chamber pressure increases when magnum primers are used.It only makes sense that adding extra energy in the form of a more powerful primer, that in turn increases the temperature will increase the pressure.Increasing the temperature in a given volume will always increase the pressure.Does the burning rate of the powder increase significantly and does this have an effect on raising the chamber pressure significantly more?That has yet to be proven.Until it is either proven or disproven,you will have your theory,and I will have mine.