Yes you have every right to have it in writing. They just don't don't want to do the paperwork and they also feel that it is a delay tatic, so they want to get anything they can from you over the phone. You don't have to fall for that. They like to intimidate because they take the chance that most people don't know their rights and such.
Do not agree to any settlement unless it's in writing. You have every right to push forward with that.