The recoil claim does have merit, as powder has mass and is being thrown out along with the bullet.
Graph below from shooterscalculator.com... 175gr bullet at 3000fps in a 9lb rifle. Only change being an increase in powder charge weight... 60gr for a 7BC, 70gr for a 7PRC, and 80gr for a 28 Nosler.
Obviously with the different performance characteristics of the above cartridges, the three rifles would have different length barrels to get the same MV and keep it apples to apples. But it shows that there's a useful recoil reduction to be had by using less powder.
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