Ok well I am claiming some American people do say it. Neither of us can speak for the entirety of our respective countries, but certainly I have heard Americans saying it on television and film.

In addition to the TV citation I gave above, see Wiktionary:

> Noun

> pizza pie (plural pizza pies)

> 1. (US) A pizza.

> [no further entries]

https://en.wiktionary.org/wiki/pizza_pie

And the slew of pizza-based results for the search term 'chicago pizza': https://duckduckgo.com/?q=chicago+pie