I couldn't figure out what was wrong with the ATP stats until the discussion in the other thread prompted me to take another look today. I started adding up how many extra points Sampras was being given by the ATP, and that was the key.
It turns out that the ATP, in a lot of its matches, counted aces and doublefaults twice in their figures for Total Points Won. The aces and df's themselves are listed correctly  but they were included twice in the other rows (e.g., service percentages, success on first and second serve, Total Points Won, etc.)
Counting them only once resolves all the major discrepancies that I've listed in the posts above.
These are the ATP stats for the 1995 AO final:
They've got Agassi winning 151 points overall, and Sampras 154, even though Agassi won more games (and won the match).
Sampras was given 154 points because his aces, and Andre's doublefaults, were counted twice.
28 aces + 4 df = 32 extra points
154  32 = 122 points won (in line with my own count)
And Agassi got his aces, and Pete's doubles, twice:
10 aces + 6 df = 16 extra points
151  16 = 135 points won (in line with my own count)
And this explains why Agassi, per the ATP, won fewer points than Ivanisevic despite beating him in the '92 W final: because he had only 9 aces while Goran had 37.
In fact all the boxscores I posted in the original post now line up with the ATP stats, when the aces and doubles are subtracted from the Total Points Won:
Quote:
AgassiIvanisevic, 1992 Wimbledon final
BrugueraCourier, 1993 French Open final
CourierEdberg, 1993 Wimbledon semifinal
SamprasAgassi, 1995 U.S. Open final
KrajicekWashington, 1996 Wimbledon final
SamprasMoya, 1997 Australian Open final
KordaSampras, 1997 U.S. Open
KordaRios, 1998 Australian Open final
RafterPhilippoussis, 1998 U.S. Open final

Almost all of them line up exactly with the ATP. With the '92 W final, subtracting the aces and df's actually leaves Goran with 157 points rather than the 159 that he has in my count and in the newspaper boxscore. It leaves BrugueraCourier with a point margin of 152145 instead of the 153146 in the print media (partly because the ATP has blank boxes where the doublefaults should go). And SamprasAgassi at '95 USO is left with a point margin of 123111 rather than what's in the boxscore and my count (124112).
So the ATP's counting is not perfect; but otherwise it lines up exactly with published figures, once the aces and df's are subtracted.
The problem is that there's no way of knowing which matches in the ATP database have mistakes, other than to check against another source. A lot of ATP stats, esp. in the '90s, are incorrect. But even in that decade there are at least a few matches where the ATP does agree with published boxscores, or with other stats (including our own counts).
The only way to confirm an ATP boxscore is to check it against stats in a newspaper, tournament website, TV network, or your own count.