Game 1:
Laker FT: 16-22
Kings FT: 16-17
Lakers Win
Game 2:
Laker FT: 15-25
Kings FT: 23-38
Kings Win
Game 3:
Kings FT: 21-35
Lakers FT: 8-15
Kings Win
Game 4:
Kings FT: 18-26
Lakers FT: 18-27
Lakers Win
Game 5:
Lakers FT: 17-23
Kings FT: 22-33
Kings Win
Game 6:
Kings FT: 18-25
Lakers FT: 34-40
Lakers Win
Game 7:
Lakers FT: 27-33
Kings FT: 15-36
Lakers Win
If anything, that proves that there was a huge disparity in Game 6 from the way that the rest of the series was called.
When you look at the style of play of both teams that year, the Kings with their slashing, cutting, back-door plays, going to the rim (remember, in the previous series against the Mavs, they had something like 122 dunks and layups in five games), then you have the Lakers running their slow, deliberate triangle offense, and only Kobe and Shaq ever really got to the line. There's a reason right there why the Kings would be outshooting the Lakers from the line.
Another thing to consider is the fact that in Games 2 and 3, the Lakers were behind late in the game and were fouling to stop the clock. In Game 3, the Lakers shot 31 threes, Kobe shot nine of them, and fouled out. Shaq finished with five fouls. They got outplayed and weren't attacking the rim in that game.
Either way it goes, you have 28 quarters in a series, and one quarter stands out, six years later, as being inconsistent with the way the rest of the series was called. There's no way to justify the Lakers shooting 27 free throws in one quarter, especially at home in an elimination game, when they had only shot 13 in the first three quarters combined. Even with the poor officiating in Game 2 of this year's Finals, the Celtics didn't shoot anywhere near 27 free throws in any quarter. The Kings got cheated out of that game, and thus, out of the series.
Bottom line.