@Dominions SonThe brain (and rest of the body) is just a machine. When you create a character, really create one, (not just giving it a name and letting it loose), you are in effect creating a virtual machine in your own head. Very much akin to taking a Windows machine (Or Linux/RISC-OS/Whatever) creating a virtual machine and then installing Linux/Mac Os/Whatever in the virtual machine. Saying that a writer is responsible for their characters actions is similar to saying the host OS is responsible for the actions of the VM OS. It's not. It supplies the framework for the VM OS to exist, the actions of the VM OS are completely out with the control of the host OS. The host machine can't even understand the language/programs used by the VM OS. A bit like a web server, a company provides web space and access, but what goes on in that space is by and large controlled by the renter.
For the less technical minded, think of Facebook. Facebook provides you with a page, what YOU do with that page is your responsibility; Facebook has little control over what you post other than to shut you down if you break a set of fairly fluid and ever changing rules set by mass public opinion.
Multiple Personality disorders along with schizophrenia, is actually quite common. But because they are 'mental' disorders rather than physical, sufferers can appear 'normal' when out and about, giving the illusion to the non-afflicted that they are just normal people and therefore it's a 'rare' affliction. Modern medicine helps many sufferers' lead 'normal' lives that enable them to slip under the radar of general society.
But you are right; those characters still want to tell their own story. If the writer wishes not to, then ultimately it's the writer's decision whether to shut the character down. Personally in that circumstance, I would let the character live and if the result is something the writer doesn't agree with due to personal beliefs/core values, then the writer has the option to create a pseudonym and post the story under the alias. Many writers do this, Tom Holt as KJ Parker, or Stephen King as Richard Bachman for instance.
I agree with Not_a_ID and their replies. And reading your replies to her/his comments makes me wince inwardly and hope that you never meet with a mental health professional at a social function. Or indeed with anyone suffering from mental health issues.