Ok maybe I just don't know exactly how it works but if the MIT license says people can sell the binary I allow for download, does the detours inside it not violate that license?
Of course it does, yes. Similarly, you could have a license saying "You are allowed to use this program to fly, by simply flapping your elbows really hard!" but that wouldn't actually make your users able to fly; that portion of the license simply wouldn't have any effect. You can't use a license to give out abilities that aren't yours to give.
As a courtesy, of course, you should note which parts of the code don't fall under your license. I suppose an exceptionally litigious fellow could take you to task for misrepresenting the copyright status of the code if you didn't clearly do that, but that's a pretty contrived scenario, and I couldn't say offhand whether that would have any actual legal merit (IANAL). My unschooled assumption is that that would fall under the heading of the disclaimed warranty of merchantability.