Then why would her face be that scarred up? Or are those scars from before at the Big Empty? Why else would the Casino staff have taken her to Vera's room? Considering that, i am guessing Dean did that to her when he locked her in the Auto Doc in the Clinic. Sinclair didn't know how to let go either, which is why he is nothing but a corpse in the pipes below the vault.
This is a poor explanation, but it's the only one I can think of that fits: the casino somehow detected their voice and used that to determine who they were. The reason being, even if Christine has been altered to look like Vera (albeit bald), Dean looks
nothing like he did when the casino was built. Also, notably Dean sounds like a normal human, not raspy like other ghouls, so I believe it's reasonable to assume that his voice in-game is the same as it was pre-war. This seems to be the only identifying feature that the two exhibit consistent with their pre-war counterparts.
As for Dog... maybe he sounded like the head chef