It was definately because the Slayer line had moved on. When Buffy died Season 1, Kendra was called, and so Buffy was passed over by the Slayer mojo. However, it does get a little complicated after The Gift, as we know from Season 7 that the Slayer line has been weakened. So what people are saying about Faith is kind of true, but for different reasons.
In Season 7, The First tries to destroy the Slayer line, by killing all the Potentials then killing the Slayer. Buffy also says that a Potential would be called on her death. Moreover, The First takes no interest in keeping Faith alive until all the Potentials are dead, whereas it does so for Buffy. This suggests that Faith in fact no longer carries the Slayer line, due to the spell Willow used to revive Buffy. The general theory is that because it had to make her a whole new body to house her soul, it also took her back to her rightful state: The Slayer. So basically, as of Bargaining the Slayer line lies in Buffy's life despite it not doing so as of The Gift.