Just saying something is (GPL/MIT/Apache/…) doesn’t make it so
blog.nig.gl
blog.nig.gl
This isn't about subsequent redistribution (and if it were, I'd agree with your skepticism). The primary distribution must also follow the terms.
You can't cherrypick which parts of the license you wish to follow.
Why's that a problem? If you own the copyright, you have the right to distribute your code, and you have the right to grant other people permission to redistribute your code under the MIT license or any other license, whether or not you yourself are complying with the terms of said license.
Relevant part:
Permission to use, copy, modify, and/or distribute this
software for any purpose with or without fee is hereby
granted, *provided that the above copyright notice and
this permission notice appear in all copies.*If you want a C analogy, saying "LICENSE: GPL" or "LICENSE: MIT" is like dealing with a void *.