Absolutely true. There's a consequence of this that people tend to ignore: You cannot remove the (e.g.) MIT license text from an MIT-licensed work if you redist

Absolutely true. There's a consequence of this that people tend to ignore: You cannot remove the (e.g.) MIT license text from an MIT-licensed work if you redistribute it as GPL. The MIT license gives you "Permission ... subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software." You can abide by that condition by distributing your software under the GPL and retaining the MIT license text for portions. You cannot abide by that condition by "relicensing" the software and removing the MIT license: you are in violation of the license.