Let's start with the base OD&D saving throw values for a 1st level fighter:
Death Rays/Poison: 12
Dragon's Breath: 15
Adding these together and averaging them gives us 14, which is also the 1st level S&W fighter's unified save number. So far, so good! Assuming a paradigm under which "good" is synonymous with "accurate," of course.
Performing the same operation for a 4th level fighter, however, gives us a value of 12 in OD&D versus 11 in S&W. At 7th level: OD&D 9.8/S&W 8. At 10th: OD&D 7.8/S&W 5. When all is said and done, the OD&D fighter would obtain his best average save of 5.4 at 13th level, while his S&W counterpart would max out at a saving throw of 4 at level 11.
If I had to speculate (always an iffy prospect, I know), I would venture that the author wanted to ensure that characters saw a steady, meaningful saving throw progression at every individual level instead of just at certain big "break points" and viewed the side effect of characters beyond level one saving significantly more often than their OD&D counterparts as a worthwhile sacrifice toward this end.
Should you happen to disagree, here's a more OD&D-accurate single save progression for Swords & Wizardry based on repeating the same calculation and rounding fractional results to the nearest whole digit for every class/level grouping:
* It is highly recommended to grant paladins a +2 bonus to all saving throws when using this table.
Bear in mind when using this system that OD&D monsters traditionally save as fighters of a level equal to their hit dice unless the DM judges them to be sufficiently similar in function to another class instead (i.e. a magic using monster might be allowed to use a magic-user's save value if it is more advantageous to do so).