Well, you can relicense the MIT-licensed code. They might have had to include the text of the MIT-licensed component license, but that would still have no effect on the license of the derivative work - it would be GPL.
Copyright would still lie with the original authors as well, after all sub-licensing allows you to pass on the rights that you already have, but does not give you any new rights.
Since the MIT license is mostly a super-set of the GPL you will lose some of the MIT parts if you sublicense but if you wish to gain more rights than what the MIT license already provides you with it will likely not work when tested in court. The best way to deal with stuff like this is to stick to the original license unless you have consulted with an IP lawyer that signed off on your plan, it is very easy to get these things subtly wrong.
The key thing to understand is that being “compatible” with the GPL means that you can take code written under an MIT license , and put a GPL license on it if you want to. The MIT license allows for this, but, the reverse is not true. The GPL does not allow you to take GPL code and change the license to MIT, and it definitely doesn't allow you to take open GPL code, and make it proprietary.