Right. I was focusing on the point that what matters is the copyright notice. While your pointing out that you can relicense MIT code because MIT is so permissive, while you can relicense GPL to almost nothing, as it's not compatible with most other licenses. However that's kinda moot, you couldn't include GPL code into an MIT licensed project anyway due to the copyleft.
(Thanks for the "ingenuous" correction, I did indeed - to my non-natively speaking brain the "in" acted as a negation to the default "genuous", which yeah, just isn't a thing of course)