(Not a teacher)
Because English has no gender neutral pronoun (it isn't used for humans, generally - perhaps an unborn baby), people tend to use 'them' and 'they' to refer to a singular person whose gender is unknown or irrelevant.
I'm not sure if it is so widespread now that it could be called 'correct', but it is certainly used very commonly. Without it, we'd have to keep saying 'him/her' or something similar, which is quite awkward and pedantic.
About 'couldn't have been', you should write 'could it have been?', although I'm not sure this works as a tag question. 'Right?' or 'is that right?' would have been suffice.
Interested in Language