Perhaps. That would make sense. By private sector, do you mean non-profit or otherwise?
I'm currently working for a public-private partnership in the city, which is where my perspective is coming from. I hear - primarily online and on forums - that having an Ivy name helps with going into, say CRE/RED. But, to be fair, when I think CRE/RED, I think Penn/MIT/Cornell.
FWIW, my SO and everyone else that I work with with Columbia degrees (3 people, albeit not in planning) told me that Columbia is NOT worth sticker price, especially if you're going into public interest work. Private sector work in RED but want to study in the city? I'd still say NYU personally.