Up to a point. I am one who is very keen to defend the weirder adaptations of classic fiction, and if Jonathon Miller and Svankmeyer are allowed to re-interpret Alice in Wonderland in surreal and post-modern ways, I can't really complain if Walt Disney does so in a crassly populist way. I think the work of art stands on its own terms Ultimately, I disapprove of Jackson's Gimli because he is crass and unfunny, not because he has nothing to do with Tolkien's Gimli.
People say that a re-working of a book can't violate the original, because the original still exists. This is only partly true. I think that Disney's Snow White did, as Tolkien says, vulgarise the Dwarves, to the extent that any fairy tale involving Dwarves struggles against the image of cute people singing "Hi-ho!" with American accents. If you liked the original mythology, that harmed it in some way. There's an old joke about an intellectual being a person who hears Rossini's William Tell Overture and doesn't immediately think of the Lone Ranger and Tonto. Is there a person on earth who can read Mary Shelly's romantic masterpiece and not see a little picture of Boris Karloff in their head every time the name Frankenstien is mentioned? At some level, then, Karloff has violated Shelly.
I don't believe that there is such a thing as the essence of Story: that, somehow, by re-telling Tarzan or Frankenstien I am "passing on" or "evolving" a bigger entity called The Story. I don't think that a story exists over-and-above any individual version of that story. Johnny Weissmuller's jungle movies were terrific fun; I loved them as a kid; I still quite enjoy them now. But they were not "making Edgar Rice Burroughs' Tarzan available to people who would not otherwise have known about him." They had almost no point of connection with ERB.
Certainly, an adaptation, done in a careful way, can hold a light up to the original. I adored Jeremy Brett's version of Sherlock Holmes: for the first time, I was seeing the character that I thought I remembered from the books coming to life on the screen. But, in truth, his portrayal was just as partial as anyone else's, taking the maniacal eccentricity (which I think is mainly present in the earliest stories) and making that the controlling feature of the character. If I take Conan Doyle off the shelf nowadays, I can read it as if played by Jeremy Brett and equally as if player by Basil Rathbone. But here, we are talking about people interpreting an existing story, not making up new ones. Brett took words which the author wrote and acting them, changing some emphasis, inventing details that the author left out (when did Holmes give up taking drugs? Doyle doesn't tell us; Jeremy Brett invented an answer.) But this is based on the assumption that the text say-what-they-say; and that a future actor or interpretor will be free to come and re-interpret them. That is a very different proposition to creating a new stories that will have the stamp of "canonicity" -- new adventures that aficionados will pretend "really" happened.
I agree with RTD the characters need to be re-invented, and a new version of Doctor Who that was simply a pastiche of someone's favourite period of the original show would be a catastrophe. Bringing back something which is nearly 20 years old implies a very substantial amount of re-invention and re-imagining. But if you re-invent Magic Roundabout as a quest narrative with villains and pop-culture references, then what you have isn't Magic Roundabout, even if the the thing is quite interesting in its own right, which, by all accounts, it isn't. There is a fine line between re-invention and starting again from scratch, between Ultimate Doctor Who and "this is just a totally new series which happens to have a time-traveler in it", at which point I lose interest.
I'm hoping that Davies faith in the mystical integrity of Story doesn't mean that he thinks he has crossed it.