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Sorry, not correct.
The BORE size of both the old and new rifles is .311". The GROOVE size may differ.
Briefly, here is what happened. The Germans first made the barrels .311" bore, .318" groove. They found that the .0035" deep grooves weren't deep enough and the lands wore and corroded badly after a short time. So they went to deeper grooves, giving a groove diameter of .323", and a groove depth of .006". (All dimensions in U.S. measurements for clarity.)
Since in any modern breech loading rifle, the groove diameter is the bullet diameter, the ammunition was changed to use the larger bullet.
When thousands of 1888 rifles were converted to use the new caliber, the Germans did not rebarrel the rifles or re-rifle the existing barrels. What they did was to simply run a new reamer into the chamber to ream the neck of the chamber. That allows the larger neck of the new cartridge room to expand and release the bullet. If that is not done, there will be a sharp increase in pressure. They seem to not have been overly concerned about firing the larger bullet in a barrel with a smaller groove diameter and in my (limited) tests, I have seen no problem in doing so.
Jim
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