The MIT licence does not require this.
The FSF calls it a "free license" [1] and I don't think they would if they didn't make the source code available.
Source code available is necessary but not sufficient for Free software, see [2]
> Freedoms 1 and 3 require source code to be available because studying and modifying software without its source code can range from highly impractical to nearly impossible.
[1] https://www.gnu.org/licenses/license-list.en.html#Expat
[2] https://en.wikipedia.org/wiki/Free_software
EDIT Oh sorry, you mean for the LICENSE to be available. Never mind then.
You are thinking of copyleft (e.g. GPL)
The license is only three paragraphs long. You can see it does not contain text supporting your claim.
For most, but not all, software. Stallman did famously argue for libvorbis, which you may know as the ogg codec used mostly by games and spotify, to be licensed under BSD instead of the (L)GPL.
But I'm willing to bet that he'd have pushed for GPL if he wasn't trying to topple MP3.
MIT/BSD licenses are pro-business - any business can take the product, change a few lines and redistribute the result without making their changes available.
GPL is pro-user - anyone who gets the source, makes changes, and then redistributes the result has to make their changed sources available as well.
It is true; the license gives you the source, to do with as you please, including closing it off.
Famously, Microsoft included BSD licensed tools in Windows since the 90s and did not distribute the sources!
And that is completely legal. If you want to force the users to distribute their changes to your open source product when they are redistributing the product, you need to use GPL.
That is why companies and corpo programmers LOVE BSD/MIT code, they can freely steal I mean use it in their for-profit products without giving anything back but some bit of text hidden in about box