It is controversial for other reasons too. A lot of psychiatrists don't believe it exists at all. They would aver that it is a type of borderline personality disorder and the actual personality split has not happened and the individual is knowingly playing a role.
The little know about it is that some people diagnosed with DID have "memory lapses" that could be attributed to other disorders. Well, it may be a real personality disorder or it may be what you said. I really don't know.