I'd like to create a basic form that, when submitted, sends a POST request to fusion tables to INSERT the data as a new row. I'd like it to be open to the public so anyone can submit the form. It seems like to do an INSERT I need to use OAuth, so the users will need to login with their google account to fill out the form. (Similar to Application 1 in the docs)
Is there a way to let users submit the form without requiring them to login? Perhaps getting a pre-generated token/secret that lets them submit to this table?
For this use case you should use Service Accounts, which act as some kind of deputy for the user. It is a technical user under your control and with permissions on the corresponding table.
See also my answers to similar questions in the past: #1 and #2