Unrelated facts I can live with. It’s contradictory and frankly misleading statements I have a problem with.
Let’s face it, they might as well know now what they are letting themselves in for before they go too far down the rabbit hole of Barnard vs Columbia status and confusion.
Sure, you can apply to both Barnard and Columbia at the same time. But, interestingly, you can’t apply to Fu (the engineering school) and Columbia at the same time. You have to choose one or the other and apply as a transfer, if you find later on, that you’ve made the wrong choice. So, again, Columbia’s arcane system of undergraduate admissions is at fault here, not you.