Because Batman does feel responsible for Rachel's death
Batman may have chosen to go and save Rachel after the interrogation, but that doesn't mean that he put his responsibilities "at ease" when he found out later, that the Joker had lied to him.
In the passage you included, this is clearly stated:
Harvey: The world is cruel. And the only morality in a cruel world, is chance. Unbiased. Unprejudiced. Fair. Your boy has the same chances she had; fifty-fifty.
Batman: What happened to Rachel wasn't chance. We decided to act. We three.
Harvey: So why it was me the only one who lost everything?
Batman: It wasn't.
He doesn't point out that the Joker had switched the location to trick them, because this had little to do with the ultimate situation. Batman thinks that by allowing Joker to thrive, he let Rachel die and Harvey Dent fall. Although the death as an event was totally on Joker, the death as the outcome was one way or another, on Batman (from his perspective).
Alfred: I prepared a little breakfast.
Nothing. Alfred sets down the tray. The envelope is propped against the silver teapot.
Alfred: Very well.
Alfred: Yes, Master Wayne?
Wayne: Did I bring this on us? On her? I thought I would inspire good, not madness-
And later on:
Alfred: Gotham needs you.
Wayne: Gotham needs its hero. And I let the Joker blow him half to hell.
Alfred: Which is why for now, they'll have to make do with you.
If the Joker had not lied, wouldn't Rachel be alive? Possibly. But his reasoning is way more complex than that. Batman feels the burden, that as Gotham's dark knight, he had to prevent all these tragedies way before, than just act at the last minute, waiting for the situation to unfold by itself.
Let's not overlook the fact that the abduction of Harvey and Rachel, happened right after the press-conference where Bruce did not find the strength to come front and admit that he was the Batman, either before or after Harvey falsely claimed that he was.
Had he admitted it, none of these would had happened (at least, in his own mind).