Suppose there is a piece of software that uses GPLv3 headers, but the code that includes said headers is not under the GPLv3 itself, but rather a GPL-compatible license, say MIT Expat. Thus the binary produced by the MIT and GPLv3 source itself must be distributed under the terms of the GPLv3.
As this "core" source is not under the GPL and as the GPL does not permit distribution under an NDA: is it in violation of the GPL to distribute said MIT and GPLv3 source (header source) under an NDA prohibiting (only) the distribution of said MIT source?
Does it then follow that it would become impossible to distribute produced binaries because the accompanying source code (tied up in an NDA) cannot be shipped with the produced GPLv3 binary (violating the GPL)?