This is false, and noted to be so by SAAMI. Note the bolded italics in the quote further down.
Velocity is a function of pressure over time. However, more than just pressure effects velocity.
Over pressure is about peak pressure, which is achieved very early.
One can have an average higher pressure curve with a lower peak pressure. Changes to the throat, groove diameter, Etc can effect that. Test barrels are cut to the minimum SAAMI specification to ensure the round is safe in every appropriately chambered rifle. This results in higher peak pressure.
When a cartridge is fired, a progressive burn of the propellant converts it to rapidly expanding gas that exerts an equal amount of pressure in all directions. Maximum recommended pressure for a rifle cartridge is usually dictated by the action strength of the rifle for which it is developed.
www.rifleshootermag.com
What SAAMI says about test barrels (Page 231
https://saami.org/wp-content/uploads/2018/01/206.pdf
"Chamber and bore dimensions of velocity and pressure test barrels shall conform to the dimensions of the chamber and bore at Maximum Material Condition (MMC) for each cartridge as originally introduced. Fabrication tolerances, however, are much reduced.
"It is recognized that
changes may be made to cartridge or chamber dimensions in order to improve the velocity-pressure relationship, accuracy or functioning in rifles as production experience indicates. However, none of these changes should be of such nature that they would cause a significant increase in pressure level of a given lot of ammunition.
"No changes shall be made to velocity and pressure barrel dimensions which would result in a reduction of the recorded pressure level of any given lot of ammunition. This would result in the possibility of future lots of ammunition being loaded with increased powder charges, which would cause increased pressure in existing rifles."
Maximum Material Condition = the condition of a feature which contains the maximum amount of material, that is,
the smallest hole or largest pin, within the stated limits of size.
Ridding someone for using a load that is 1 gr under max powder charge per the manufacture is silly.