That is correct. The original 1888 rifling proved too shallow and was rapidly washed out. The Germans gradually increased the groove depth, but finally decided to increase the bullet diameter and the groove diameter, which they did c. 1905. (The groove (and bullet) diameter was increased from .318" to .323"; the bore diameter remained .311".) I have read and have said that Model 1898 rifles with the old barrel dimensions were re-barrelled but someone demanded absolute documented proof of that and I don't have any, so I will say only that it seems to make sense.
In any case, the old 1888 rifles were not rebarrelled; those in good condition had a new reamer run in, expanding the leade diameter and chamber neck diameter. The latter is critical. If the chamber neck does not allow the case neck to expand and release the bullet, pressure goes way up.
The conversions of Model 1888 rifles to use the new cartridges and clips was done in Germany for the German war reserve, and many were issued to German reserve units during WWI. After WWI, many of those converted rifles were sold to Turkey, where they received Turkish markings; many collectors assume that the conversions were done in Turkey, but as far as I can determine that is not true - they were done in Germany.
Jim