If you're on an untrusted computer, the network is by definition also untrusted.
What happens if the computer has a hacker's self-signed certificate for https://accounts.google.com installed and the hacker sets up a man-in-the-middle style attack?
The hacker's browser asks Google for a QR code and it gets sent to your browser. When you scan the code and authorise from your phone, the hacker's browser would be logged into your Google account.