If I take some code I don’t have a license for, feed it to a compiler (perhaps with some -O4 option that uses deep learning because buzzwords), then is the resulting binary covered under fair use, and therefore free of all license restrictions?
If not, then how is what Copilot is doing any different?
No, the binary is not free of license restrictions. Read any open source license - there are terms under which you can redistribute a binary made from the code. For GPL you have to make all your sources available under the same terms for example. For MIT you have to include attribution. For Apache you have to attribute and agree not to file any patents on the work in Apache licensed project you use. This has been upheld in many court cases - though it is not always easy to find litigants who can fund the cases the licenses are sound.
Because the sources used for input do not belong to the person operating the tool.
If you say that doesn't matter, then you are saying open source licenses don't matter because the same thing applies - I could just run a tool (compiler) on someone else's code, and ignore the terms of their license when I redistribute the binary.