If the Mark III Ross is assembled correctly, or if it has the "pinned" bolt, it is quite impossible for it to get out of adjustment. To throw the rifle out of adjustment requires HUMAN INTERVENTION.
An action which would handle 125,000 pounds pressure or higher likely is not going to be bothered by just about anything modern you can put through it. I know where there is one which has been rebarrelled to handle 7mm Rem Mag (a 60,000-pound+ cartridge) and it works fine. Remember, that load is spread out through SEVEN locking-lugs!
For a Magnum-class cartridge, the Bolt requires NO work; the rim of a .303 is the same size as the rim on a .280 Ross or on a 300 WinMag.
Remember, the rifles were sold, more than a century ago, chambered for the 280 Ross, which had an OPERATING pressure of 68,320 pounds and a Proof pressure of 80,000 or a bit more. The common military action is identical in every way to the action of the 280 Sporters. The Ross Rifle Company did not make military actions and sporting actions: they just made ACTIONS and then used them for whatever rifles they required for the market at that time.
On the chance that you get a rifle with a replaced Bolt or Bolt-head, it is good to know that the actions originally were factory LAPPED to provide an even bearing on all 7 lugs. This is important for the highest absolute strength and for the finest obtainable accuracy. When rebuilding a trashed rifle, checking the action for even lockup and, if necessary, lapping it, can be important.
Safety? I have been shooting Rosses for a bit over 50 years now. I still have all my fingers and both cheek-bones. SOME would say that that is unfortunate, but they are not as attached to those parts as I am! I think that Rosses are just fine!