I nearly fucked up Fizzbuzz on a tech interview once, but managed to pull it out at the end. Later someone told me the guy who interviewed me said it was one of the best interviews he'd ever done.

It kinda makes me doubt it as a screening tool.

Thank you for sharing.

How can one administer fizzbuzz over the phone?

In a Google doc. While you may say a Google doc is a suboptimal environment for coding, it was literally fizzbuzz.

Just do it in Python:

import fizzbuzz

fizzbuzz()

If someone did that, I'm not sure whether I would give them brownie points for not reinventing the wheel or demerits for being a smart ass.