What weirds me out is that it seems few US corporations care that they don't have copyright to their synthesised code, if the rumours regarding this are correct.

If you don't have the copyright, then you can't license or litigate it under the common rules of software. If someone 'steals' it you can at best go after them with some trade secret case, and I suspect this would be limited if you had already shared the code with them, e.g. because they helped you synthesise it.