I am having difficulty proving that the salary changes have a net effect of zero. I'm not sure how they are handling players with multiple teams in the same year. If I assume they only count one combined version of that player, then I get the following results...
39,858 Total Hitters
9,506 increase salary (+105,507,108 million or 11,099 per player)
29,829 decrease salary (-108,333,183 million or -3,632 per player)
523 same salary
Total salary difference: -$2,826,075
28,585 Total Pitchers
5,149 increase salary (+58,312,570 million or 11,325 per player)
23,347 decrease salary (-52,316,848 million or 2,241 per player)
89 same salary
Total salary difference: +$8,717,737
Overall salary difference: +$5,891,662
If I include all versions of multi-team players, then the overall salary difference is -$26,065,742 (so this clearly isn't what they are doing).