I feel that you both are right. I too was disturbed by the lack of Bruce's parents haunting him in The Dark Knight. I did feel that Rachel was sort of a link to that area. However, I think Nolan was more interested in exploring Rachel's key assertion to Bruce:
"That Bruce needs Batman more than Gotham needs Batman."
This to me is the core of that movie. Think about it.
The main dramatic question character-wise for Bruce Wayne is: "Does Batman know his limits?" The theme is explicitly stated when Alfred warns Bruce to "know your limits" and Bruce replies with "Batman has no limits."
The Joker's rise to power via the mob hiring him has EVERYTHING to do with Batman not knowing his limits. He tells the mob: "Batman has no jurisdiction." At the First Act Break, Batman proves The Joker right by breaking international law and traveling halfway around the world to apprehend the mob fiancieer. This kicks into action the whole thrust of the main movie:
How much chaos and death can The Joker cause before Batman unmasks himself? Remember, this is the threat made by The Joker. And he proves to be a man of his word...
He kills judges, commissioners, DAs, random city workers, mobsters, police officers, blows up Gotham PD, and blows up a hospital all to solidify his power over the mob and to push Batman to his breaking point. Time and time again, The JOker's right: Batman refuses to take off his mask and instead lets more and more people die because, as Bruce says, "Batman has no limits."
Nolan is asking the question is this right? How is this sane? Remember, Bruce started to be Batman as a temporary job to inspire hope in Gotham. Nolan's films seem to be leading to an exploration on how someone becomes trapped by their altruism when that altruism is founded in grief and anger and vengeance. No rational man would decide to wage a life-long war on crime. What's tragic is to watch a man become trapped by his own obsession as he becomes blinded by his own addiction...
Rachel is right. Bruce needs Batman, and is so addicted that he allows nearly 30 plus people to die both directly and indirectly because of his stance. But that's not the most important death, and the most important death is key to the tragedy that Nolan is outlining here.
Many people ask: why was that scene in the warehouse at the end necessary? Well let's look at it:
Batman arrives and is surrounded by his two closest allies: Gordon and Dent. A very significant moment occurs when Dent cries out: Why was it only me who lost everything?"
There is a long, significant pause by Batman before he says "It wasn't."
Isn't that a rather weak answer? Why, at this moment, did Bruce not unmask himself and shock Dent back from the brink with the revelation of who he was and what he's lost? But Bruce doesn't. No. Because he is so addicted to being Batman, so lost in the persona, that even while in front of two people he should be able to trust, he refuses to and instead allows Dent to go over the edge (literally).
But notice that Bruce does realize this. As he stands over Harvey's dead body, note that when Dent rambles about the Joker winning, Batman very pregnantly looks up toward the warehouse level where he and Dent and Gordon faced-off, and then back at Dent's body, realizing that he didn't even think to take off his mask and show Dent that he wasn't the only one.
It's a significant, subtle moment when he looks back up, but it's the only explanation for why Batman does it. He finally understands what he's become, that Rachel was right, and that all those men died. Again, through the action of falling (as he does as a child into the bat cave), Bruce has become something else...
After he looks up, he delivers his lines: "I killed those people."
And he did, in a way. The blood is on his hands. So now the vigilante, he takes off, forever trapped by his own obsession to avenge crime since he helped ruin the only hope he had at ever escaping his quest.
It's ultimate a massive tragedy about one man's obsession and best intentions.