I have experienced the same issue. It’s sad to know that there are posts from over a year claiming the same problem and yet nothing was resolved.
Aside that, I can’t switch permissions as well. Even though I have selected Read and Write as soon I click the update buttom it switches back to Read Only. Annoying and desapointing Twitter problems that doens’t have any solutions for its users.
Let’s hope someone from Twitter crew come here and give a real solution or fix for good all these stressfull bugs.