Naruto "saw through her lie" when she mentioned Sasuke. Before than he looked to have actually believed her. Naruto still believes in the old Team 7, as shown in his flashback.
Hinata only sees the Naruto that's openly shown. She knows nothing of his suffering of being a Kyubi host, for example. It's Sakura that sees closer to Naruto's strength and real character.
It's also Sakura who shows Naruto more appreciation.
Naruto would have lost his mind regardless of who jumped in to save him. Hinata was a friend who got "killed" before his eyes. That's the oly relationship they had.
Although I agree that Hinata doesn't Know Naruto as a person as well as Sakura, you are wrong in assuming she doesn't know his suffering for being the jinchuriki. If you look back at part 1, it was exactly because of his attitude regarding his situation that got Hinata's attention and admiration. All she saw was a kid whom was casted aside by everyone all the time, and still that kid moved on, and improved himself. On the other hand we have Hinata, always been the target of critics from her father and clan about how "weak" she was, and how undeserving she is of being in the main family. Their situations though based on different reasons had a great similarity, for both had to prove their worth thru actions.
On this subject, Sakura is completely clueless, for she never experienced this kind of prejudice. Just remember that until the beginning of part 2, when they went to help Garaa, Sakura didn't even understood the full extent of Naruto's feeling about a fellow Jinchurikii.
On the appreciation issue now, I fail to see how Sakura shows Naruto any appreciation. She goes to kill Sasuke and find herself lacking, only to have Naruto save her. What did she do? Nothing. In part 1 when Naruto saved her from Shukaku/Garaa, what did she do? thanked Sasuke for saving her. If we pay close attention to the first part, Sasuke only gave Naruto any attention because he was as interested as she was in saving Sasuke. But that was then.
Back to the present now, until I few chapters ago I was quite sure Sakura would end up with Naruto. The story had been developing in a nice and steady way that would/could point to that possibility. However, 3 things have shaken my belief.
First of all, as mentioned before, the shinobi that approached Sakura to tell her she was wonderful and all, blah blah, etc, and she is thinking of Sasuke; not Naruto. This was the hell of a hint that Sakura Loves Sasuke, period. It seems nothing will ever change that, no matter how much some of us want it too.
Second, when Naruto showed up in the battlefield to help identify the white zetsus, not only he saved Hinata, but he actually her feeling, and how she was for being unable to stand up on her own. Not only Naruto acknowledge that, but he also took the time to speak to her and to tell her exactly what she needed to hear. At first I thought this was Naruto following Itachi's suggestion, of acknowledging his fellow Shinobis, but than I realized that it might be something else since it was Hinata we are talking about, and he knew her well enough to know what she was feeling.
And Last, but not least, in the last chapter we had all those declarations from the konoha shinobis. I loved Chouji's by the way. As Hinata was expressing her desire to be "by his side", Sakura only mentioned to be there for him along with everyone else. It may seen little, but the wording is quite significative. To be by one's side is to be there for the one, no matter the odds. Hinata didn't say anything regarding her love or feelings for him, though they are present in her tone, but above all, she meant that she would never let go of him (if I compare de words with other sources - bad translations included.

. Yet Sakura is just along for the ride with everyone else.
I won't say it's a fact, for those are my observations and how my view of the situation has shifted. It may be that Kishi intended it this way, only to reverse it again further down the road. Or it may just as well kill everyone and Tobi use the Moon genjutsu on the entire world.
True love gives,it dose not demand taking.Hinata gives freely and ask for nothing more than acknowledgment in returned, Sakura just takes and takes. Naruto is more like His mother in temper,speech and character, Hinata is more like Minato the quiet type and now both are evolving their personalities more and more but Sakura still is the same,She has yet to mature in Her view of the way things are and are becoming. Theirs Reasons why Kishi is developing Hinata's personality more and more and leaving Sakura behind in Her personality development. You may not like it, but you can't change it either. All you can do is accept what you can't change, you can only change what is in your re power to change.
I second that...
/Cheers