Correct. And the combined work needs to carry the MIT license text and copyright attributions for the MIT software authors. With binary distribution it must also be overt, not hidden in some source code drop, but directly accompanying the binary.
Many people who talk about relicensing never credit the MIT developers or distribute the MIT license text. "Because it's GPL now."
I don't think that you believe that, but many developers do.
Some don't see the need for source code scans for Open Source compliance, because the license.txt says GPL, so it's GPL. Prime example is the Linux kernel. There is code under different licenses in there, but people don't even read https://github.com/torvalds/linux/blob/master/COPYING till the end ("In addition, other licenses may also apply.") and conclude it's simply GPL 2 and nothing else.
Also be aware that sublicensing is not the same as relicensing.