I know Enfield barrel Martini's usually came with a new breech block having a smaller diameter firing pin so as to avoid the possibility of rupturing the primer. It was found that the older, larger firing pin tended to do so due to the higher sustained breech pressure. It is also possible that the replacement breech blocks were of a higher grade of steel and less likely to deform under repeated firings using cordite loaded rounds. Other than those guesses, I can't tell you a whole lot more and it is too bad Greener doesn't explain in detail what he meant in his book.
The usual 303 MkVII round develops an operating pressure of a round 49000psi, while the 577-450 Martini Henry round has an operating pressure of around half that, so it is possible that, with the smaller base diameter of the 303, the older breech blocks might take a greater hammering over a smaller surface area and deform more.
Their shoulders held the sky suspended;
They stood and Earth's foundations stay;
What God abandoned these defended;
And saved the sum of things for pay.