This sure sounds like an echo from the past. When the M1903 was the American service rifle and target shooters were very familiar with the thing, American shooters were very proud of the thing. They rightly viewed the Mauser action as a rival and in print, pointed out differences between the Mauser 98 and the 03 Springfield to make the case that the American made and designed 03 Springfield was superior to the Mauser. The primary focus of the hype was the claim that the 'superior" workmanship of the 03 Springfield made it a superior action and bolt "slop" was one of those criteria they used back then to determine the perfection of an action. The M1903 action had less bolt slop, when the bolt was open, than the M98 Mauser. Ergo, to the American mind, that was proof that the M1903 was superior to the M98.
Having shot both M1903's and M98's, I have a M98 match rifle, I can say that in every point of departure from the M98 Mauser action, the American M1903 is an inferior action. I have broken firing pins, cocking pieces, firing pin collars, ejectors, and extractors in the M1903. I have replaced a number of gouged bolt stops and bolts with battered left locking lugs. The Mauser has a nice cushioned bolt stop, whereas the M1903 uses just the tip of the lugs against a hard bolt stop. The M1903 is a very unreliable action. The M1903 has about zero shooter protection features in case of gas release. I shot my first Colombian Mauser enough to wear out the case hardened surface in the bolt cocking cam, and that was the only part that wore out. I operated the thing in rapid fire sequences for years and I can't say that bolt wobble made that much of a difference in operation.
I do like my M70 action and that action was designed in the era when Americans decided an action was good or bad, based on the amount of bolt wobble. My M70 has very little bolt wobble. I like the M70 action as it is smooth and slick in operation. Bolt wobble gets to be a problem when there is too much wear in the receiver and the bolt cramps. The one rifle I have that has this problem is a Rock Island Arsenal M1903 Sporter. The receiver is worn and the bolt cramps and I can't push it as fast as I want.