A common misunderstanding, but no!
You can incorporate the MIT project into your X-licensed project, and now have three parts you need to consider: the MIT project, your X project and your (presumably x-licensed) composition of the other two projects.
It means, for example, that when distributing your composite project, downstream users do not only have to comply with X, but also with MIT (for that part). So they havbe to reproduce the MIT license (they would not need to do so if you truly relicensed the code!), and they need to distribute the copyright marks of the MIT project etc.