Elizabeth's Brooch - follow-up question

Spoilers within. Finish the game before reading on.

I've already learned that it doesn't matter which brooch I pick. But I did notice that at the end, the Elizabeth that drowns me in the baptizing pond doesn't wear either brooch, just an unadorned neckband. Is this an oversight or what is the meaning of it? She still wears it on the way to the lighthouse. Did the brooch go missing? Did she take it off? Or was my Elizabeth at some point replaced by another, and how/why?

Solution 1:

Well, there are multiple theories about this and only one that make somewhat sense:

The theories that she took it off or that it was a oversight by the developers don't make any sense. Even if the brooch doesn't change the plot it's still, weirdly, a important plot point.

The other theory is that by drowning Brook, Colombia doesn't exist and so stuff starts to... huh, disappear. Doesn't make sense either since Elizabeth would disappear sooner and the brooch was given by the Lucete. That might give it some "time wibbly wobbly" effects.

The last theory, that I know of, is that she wasn't Elizabeth. Not your Elizabeth. Booker confirms this in the dialog when he doesn't recognize her after some moments of confusion. This brings the question on where is Elizabeth or perhaps she is all of them.