This is usually a misunderstanding of permissive licenses.
You can't change the license of the code, even if that license is permissive enough for the code to be incorporated in proprietary works.
I mean, often this doesn't really matter because, unlike with GPL, publishers are not required to give you the source-code. But it matters when that source-code gets republished, say, under a source-available license, after having been under MIT/BSD/APL2, in which case, that's illegal, unless the company owns the copyright to do so.
As an example — if you have a file with a copyright header saying the code is licensed under a permissive license, you can't just change that header to a different license. There's even a famous case about it: https://undeadly.org/cgi?action=article&sid=20070913014315
It all comes down to copyright. If you copy a piece of code that's not trivial, even if the license allows you to copy and reuse that piece of code, you're not suddenly the copyright owner of that code. Permissive licenses are permissive, but they do have restrictions, and most importantly, with copyrighted works, excluding the fair use cases that depend on legislation, you can only do what the license allows you to.
So, no, code licensed under permissive licenses can't be re-licensed as proprietary, even if it can be incorporated in proprietary works. And this is often a useful distinction to make, as I can think of several re-licensed projects under source-available licenses that couldn't have been re-licensed without copyright assignments.