I've talked to a whole lot of actual experts at several of those companies over the years and not one of them has said that.
Nosler in fact charges extra for their fully prepped and weight sorted brass.
Variations in wall, shoulder, and neck thickness mean differences in weight and they also will correspond to differences in volume.
Sort, don't sort, sort by weight, sort by liquid volume, whatever suits you but let's don't have any more passing off of bad information as gospel. It doesn't help anyone.
For the average hunter and reloader it probably won't make enough difference to matter but then they are just trying to hit a 10" target at a maximum of 200yds.
For long range precision shooting it's one more variable that is within our control so it's worth doing.
I have had multiple manufacturers tell me weight sorting is not accurate. I repeat several. I am not going to say who on this open forum. It is what made me check in the first place. With most of the available brass manufacturers I have checked each individual case using both methods and, as stated several times, I found the statement to be false. The es and sd of weights was so close(within a few tenths of a grain) I will never measure volume again unless just checking for comparison between different cartridges.