Why do people say this?
How many millions of AR-15/M-16 type rifles have come from the factories with a "flash suppressor" attached to their muzzles? The .223/5.56x45mm cartridge can hardly be considered a heavy recoiling cartridge.
All a flash suppressor or muzzle brake is, is a tube with holes in it's sides that is attached to the muzzle of a firearm. The shape, size, and number of holes varies, but they both do the same thing: they allow some of the expanding gasses to exit to the side of the muzzle a few milliseconds before all of the remaining gasses exit the muzzle.
It's hard to define what a "magnum" cartridge is, but basically it has more capacity than a "standard" case so it can burn more powder. Burning more powder increases velocity, noise, and recoil.
When I shoot .357 mag cartridges in my .357 mag pistols, they are way louder and have more recoil than when I shoot .38 spl cartridges in those same pistols.
OK, enough of my rant on muzzle brakes, and back to the OP's original question.
Like Big Uncle also posted, "Try shooting someone else's .338 first..." We are all built differently, we each absorb recoil differently, and each rifle will recoil differently depending on tis fit, weight, and shape. Five people can shoot the same rifle, and you can get five different opinions of how hard the recoil was.
I like to shoot, and I shoot a lot. When I was competing in registered Trap, I was shooting 10,000 12 ga shells per year. When I was competing in registered Skeet I was also shooting 10,000 shells per year, but they were not all 12 ga. I also don't like heavy recoil.
To reduce the recoil in my shotguns, I made several modifications to them. These modifications would also apply to reducing felt recoil in rifles.
First, the gun should properly fit the shooter. Length of pull and shape and drop of the comb of the stock are not too difficult to modify.
Many after market recoil pads like Limbsaver, Decelerator, and Kick Eez will "absorb" more recoil than many factory pads.
A heavier gun will kick less than a lighter gun, all else being equal. Weight can be added to a gun with lead or by installing an in-stock mercury or mechanical recoil reducer.
And finally, the barrel can be ported or a muzzle brake added.
I have done a combination or all of these things to several of my shotguns, and to my .375 RUM and .300 Wby rifles.
Out of the box, my .375 RUM kicked harder than any gun that I had ever shot. After the modifications, it's kick does not feel much more than my basically factory 7mm Rem mag.
And with the modifications, my .300 Wby does not feel like it kicks as hard as my factory .270 Win. Last year in South Africa I let my PH shoot my .300 Wby off the bench, and he said that it did not kick as hard as his 7x57. I will often take my .300 Wby to the range and shoot 20 or more shells through it then go over the the Skeet range, shoot 100 or more 12 ga shells, and have no soreness at all from recoil.