The fact that Hinata wanted to interfere with the Pain fight isn't the problem that I have with her confession. Naruto clearly was in a bad spot and needed help. My problem lies in her intentions behind jumping into the battle. She didn't do it to save Naruto; she did it to confess her feelings so that she wouldn't have any regrets.
Hinata knew that she was no match against Pain; she knew that jumping down there all by herself would be pointless, but she did it anyway.
If saving Naruto was truly what she wanted to do, then as a ninja, she should have been trying to come up with a plan to get Naruto out of that pinch. At the very least, she could have tried gathering other people to assist her. No one else was going to jump in after her because only the Hyuuga clan could actually see what was going on, and most of them were injured, unconscious, or dead. Her guard, for example, was down with a broken leg. That's why he couldn't stop her from leaving, and as we know, Neji was away from the village. Everyone else was blind to what was happening to Naruto - that's why no one else was trying to save him. (Plus Naruto had told everyone to believe in him and stay out of it...) She knew that, but still she didn't try to round up a team of less injured shinobi to go down there with her. Sure, a group would still be nothing against Pain, but they could have at least caused enough of a distraction for her to get the rods out of Naruto's arms. That was all she needed to do, as he could have pulled the rest out himself.
That didn't happen though. So now we have Hinata standing in front of Naruto with Pain, an enemy that was capable of completely crushing the village, staring her down. There were still other things that she could have done to save Naruto in this situation, or at least tried to help him with. The anime team pretty much covered the possibilities with their filler version of her confession. The first thing that filler Hinata does during her confession is attack the rods in Naruto. If saving Naruto was what she wanted to do, that would have been the obvious course of action, but canon Hinata doesn't do that.
Canon Hinata either wasn't trying to save Naruto, or actually thought that charging at Pain was going to do something to save Naruto, which clearly wasn't the case. Because I don't want to completely lose all hope in Hinata as a character, I choose to believe in the first option. All she wanted to do was confess to him so that she would have no regrets later on. She wasn't thinking about what she would do to help him after she confessed. She just wanted to get her feelings off of her chest as she thought that was her last opportunity to do so. That's what makes her confession selfish instead of selfless. She was acting for herself, not for Naruto. She didn't have his well-being in mind. If she did, she would have stopped to think about how witnessing a friend being murdered in front of him, while completely powerless to stop it, would have affected Naruto. Kyuubi or no Kyuubi, she had to have known that that wouldn't have affected him in a positive way, but she chooses to charge at Pain anyway.
The last point I want to make is that Hinata had no way of knowing, prior to jumping down there, that Naruto was going to unleash the Kyuubi's power. I don't even think she knew that Naruto had the Kyuubi in him at that point. This proves that she had no intention of saving him. Remove the Kyuubi from the equation and what was her plan? To jump in front of Naruto, (despite her guard telling her that she would only be in the way), confess, and charge Pain, all the while knowing that she stood no chance against him. None of which had anything to do with actually helping Naruto out of his predicament. Had it not been for the Kyuubi, Naruto would have been left in the exact same position that he was in before Hinata chose to "save him". Pinned to the ground with Pain standing over him. The only difference would be that Hinata's mangled body would be laying a few feet away from him. Nice one, Hinata.
She's lucky as hell that:
1) Naruto went Kyuubi, because ultimately that's what saved him.
2) He didn't accidentally step on her or pick her up and fling her mangled body into the horizon.
3) He was drawn away from the village, leaving what few survivors there were alive, (which was also thanks to Sakura having everyone evacuate)
4) Sakura was able to save her before it was too late.
5) Minato was there to save Naruto from being completely overtaken by the Kyuubi.
This was all pure luck. Hinata had no idea that any of this was going to happen.