> Where does the GPL say you have the freedom to relicense code or derivatives under MIT by fiat?

The first part of this sentence (where in the GPL) is unreached if the second part of it is unmet (relicense code or derivatives) which I contend it likely is. You're begging the question.

However:

> The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work

earlier:

> A “covered work” means either the unmodified Program or a work based on the Program.

It's that element that would be difficult to prove "work based on the Program"