This is false. I run the A191 chambers, they have SHORTER throats than SAAMI chambers, therefore a SAAMI chamber produces LESS pressure.
To the OP, the reason the factories produce loads that work in almost every gun is because they use a few techniques that are known to produce high start pressures with a fast powder that produces a flatter curve.
They blend several powders to get a pressure within 10,000psi of max at the VELOCITY they determine to be optimum.
The biggest trick they use is crimping, this raises the start pressure significantly and flattens the curve somewhat. The rise over time is short, because the powder used is on the fast side.
I compared Winchester loaded ammo in 300WM loaded with 785, Winchester's equivalent to 780, and my own 780 loads.
I could not come close, without excessive pressure, to their velocities. Over my pressure trace, my loads were over 75,000psi, proof loads actually, to match their velocity.
So their tricks in formulation, crimping and blending is what makes their loads safe.
The maximum pressure from any load in that factory ammo was only around 56,000psi, now I know my pressure trace isn't calibrated to SAAMI reference ammo, but that is quite low for the 300.
Cheers.