Oh, I attribute Rowling's offensive misinterpretation to pure ignorance! It is much the same as when American authors try to write things set in past cultures and times in Britain and Ireland and get things terribly wrong.
As someone working on a story that draws from a number of cultural sources that are not my own, including Japanese culture... which... lets face it... tends to be romanticized to an insulting to degree by us Americans... I like to think that its not as simple as "People are always going to fail at writing about things from different cultures."
I think its more, as others have said, that one has to do the legwork. Its more to say that "Lazy people are usually going to fail at writing about things from different cultures." Any and all foreign cultures I plan to draw from for my story are cultures I either know a lot about, or plan to learn more about and adjust my writing as needed.
But why? Why is this somehow worse than Braveheart or the literally thousands of books and movies that use Christian mythology for their fantasy universes? I'm not a fan of the Catholic Church but you have to admit they get used as a plot device more than basically any historical organization in the universe.
Braveheart falls under the same category as The Last Samurai for me. Its an entertaining and enjoyable movie, so long as you go in with the acceptance that its not even remotely accurate to its setting.
The difference, though, is that the Scottish and the Japanese are both prominent groups, with no shortage of sources you can turn to for historical accuracy. Christianity, as well. In fact, in Western culture, Christianity is widespread and pervasive. There is no shortage of clergymen willing to correct any misgivings you may have about Christian ideology.
Native American cultures, on the other hand, have a long tradition of persecution, genocide and cultural appropriation. They went from being the dominant cultures in America, to being pushed to the verge of extinction, in a very literal sense. Then, to add insult to injury, their beliefs and traditions have been constantly misrepresented, and often even used as a joke. I mean, for crap's sake, the Redskins are a thing. They're STILL a thing. Even though basically everyone has been begging them to change their name, they're STILL the "Redskins." Hell, in the Lone Ranger, Johnny Depp was basically doing redface. In 2013. (Yes, he argued that he has "Native American ancestry", but so do a LOT of Americans. Hell, I do too.)
The fact of the matter is, in America, and I'm sure the UK isn't much better, most people BELIEVE the fictional versions of Native culture they've been fed.
I'll be honest. When I first heard this story, I didn't get the outrage either. Instead of just plugging my ears and going, "if I don't get it, its not offensive", like some people do; I took it upon myself to figure out WHY its offensive, and... yeah... once you really start to grasp the level of both literal and cultural genocide that the native people of America have faced, and the offensive ways that their culture continues to be appropriated even to this day... its not that hard to understand why they're so upset.
Its easy to go, "If its not offensive for x, its not offensive for y", but that rests on the fallacious assumption that all cultural groups have had the same experiences.
As others have said, it boils down to context. Too often, people seem content to ignore context and nuance and pretend that a one-size-fits-all solution will solve every problem: Treat every group the same, ignore historical context, and then everything will get better. Its the same sort of outrage you'll often see whenever people try to support any historically disenfranchised group. Try and support black people, white people accuse you of being racist. Try and support women, men accuse you of being sexist. At the end of the day, you have to realize that the world is full of nuance, and full of gray areas. Not every group of people has had the same experiences, and as a result, not every group has the same degree of power. If we ever want TRUE equality, we need to acknowledge that, and do what we can to even the playing field; we can't simply pretend the playing field is already level and then get angry when people try to point out that its not.
... and I just NOW noticed that Gadifriald already covered both the Johnny Depp thing AND the Redskins thing... ah well.
As for Twilight, I find that offensive on a far more existential level, much like the existence of Jar Jar Binks.
Edit: Actually, I take back what I said about Braveheart. Its been a while since I watched it and I think I blocked out the last time I tried watching it as an adult. Come to think of it, it's... not even all that good really. I mean, not even taking into account the rather offensive (and historically... questionable) portrayal of the Prince Edward.