Nolan's Batman trilogy may have been darker, but it did not exactly nail the original spirit of Batman as a character. Nolan's franchise was about a man who, as an adult, decided he wanted to stop organized crime, and who was willing to give up that fight when he'd beaten it, not about a man who dedicated his entire life to fighting crime from a young age. That's an important distinction to make when discussing the original "spirit" of Batman as a character. If anything, Nolan's franchise has far more in common storywise with the 70's and 80's and YEAR ONE era versions of the character, with a dash of THE LONG HALLOWEEN and trace elements of major modern stories like KNIGHTFALL, NO MAN'S LAND, etc.
I would argue that BTAS is a more comic accurate than the 60s series, because the 60s show represented the Silver Age but BTAS encapsulated pretty much all the eras up to that point, including the early Kane/Finger stuff, with the art deco style and the use of some of the classic Joker stories from that era. It used many specific comic storylines as a reference for episodes, and Denny O'Neil wrote the Ra's al Ghul episodes, etc. And when the Timm/Dini-verse moved into Justice League, that is where they got more Silver Age-y.
Exactly, and BATMAN: THE ANIMATED SERIES and TNBA also incorporated elements from the various films, and went on to influence the comic books themselves with regard to designs and new characters, locales, etc. Though it should be noted that the original Batman TV series also used quite a few comic book stories as source material, much like LOIS AND CLARK did in the early 90's.
I think people look at West's BATMAN and yes, it's campy, but it is not a blatant parody of the source material. It's a satire, with some elements of parody. For all that, it's largely written and played straight, which is why it works as well as it does. Its just campy as hell because of the content. If you read a Batman comic from about the mid forties to the sixties, the show pretty much nailed the tone, the story approach, and the characterization of Batman. Actually, the show presented a fairly grounded version of what the comics were, because it largely ignored a lot of the wilder science fiction/fantasy stories that were being told in the comics at the time.