I'd rather that Twitter didn't break my back button. But I see no value in having a global back button anyway. Who should my browser's back button sometimes take me to the previous page, sometimes take me to Microsoft Word, and sometimes drop me on the desktop? Why can't the back button do one thing right instead of a bunch of things kind-of right?
And I would much rather have no global back button on my phone than a sometimes-broken one.
It makes sense with the way Android works. Applications are often interconnected. I can browse to reddit in Browser, click on a YouTube link and open it in the YouTube app, hit share, and open up GMail to send it to a friend. I can then hit back to go back to YouTube, then again to go back to reddit. Believe me, it feels so natural to me now that I find iOS clunky to use without it.
But you can't just ignore the back button, because apps use it rather than providing their own back buttons. You have to use it, and there's no way so far as I know to force to behave in a way I would consider intuitive.
How it would that's intuitive to you? The back button should return you to whatever previous screen you were on -- that's pretty intuitive.
As for applications that get it wrong; that happens on all platforms for all kinds of different features -- it's unfortunate but it shouldn't reflex poorly on the feature itself unless it's particularly hard to implement correctly.
And I would much rather have no global back button on my phone than a sometimes-broken one.