But when he came out of the Framework, he was himself again, not the Doctor? In our world, the Doctor didn't appear as an alternate personality this way?

[She's not trying to skip important details, exactly, but she does want to be clear on some of the facts of the story.

She wants to be clear about the nature of this version of Fitz so she can understand what safeguards they can implement to prevent this from happening again.]

What does this have to do with his brain injury?