Your question is confusing as you appear to be conflating two distinct concepts.
The first concept is publication, or the wide dissemination of your dissertation. If you didn't publish your dissertation, then nobody could use your words, or even your ideas, because they wouldn't know what those words or ideas were. Publication is required for research to enter the body of public knowledge that everybody can use. If you don't publish it, you might as well burn it for all the good it would do the rest of the world. It still, of course, might do you a whole ton of good because you used it to show that you deserved your PhD.
The second concept is copyright. Copyright is typically about restricting what others can do with your words and owning a copyright on your work makes it harder for other people to build off of it, though not impossible. Copyright typically only affects a specific expression of an idea. If someone else expresses the same idea with different words, copyright doesn't prevent them from doing so.
In the United States, you are automatically granted the most restrictive possible copyright on anything you create. You then negotiate with various parties to allow them to make copies of what you made, usually in exchange for some sort of compensation. There are some interesting wrinkles here like "works for hire", but that's basically how it works.
Derivative works are tricky in copyright, and it depends a lot on the nature of the original and the work based on that original whether or not the new work will be considered derivative.
For example, most Harry Potter fan fiction would be considered a derivative work of J.K. Rowling's original story. Her characters are covered by a rather amorphous blob of protection.
But an academic paper with significant new results would not generally be considered derivative of a different academic paper that it used as a base or jumping off point. Conversely, an academic paper that had nothing new or significant in it that copied large sections of a different academic paper might be considered plagiarism, and would be a copyright violation. Similarly, a book review that quoted a few select sentences or maybe even a paragraph of the book it was reviewing wouldn't be considered a copyright violation unless the review consisted almost entirely of quoting the book and added little or no commentary of its own.
This sort of use of another work in a new creative work falls into an area of copyright law called "fair use". Fair use is a very tricky area of copyright law, as what is and isn't fair use tends to be up to the discretion of a particular judge or jury. And it is also strongly affected by the general standards of the particular area of creativity that is being judged.
So, in short, copyright is largely irrelevant to whether or not other academics can use your work. The standards of academia over time would play a large role and most judges would decide that any use that wouldn't be considered academic plagiarism would be considered fair use.
But, publication is very relevant to whether or not other academics can use your work.
By conflating them, it sounds like your school is trying to pull some kind of fast one.
My guess is that they want you to publish in a journal that requires you to sign over your copyrights to them with no compensation. Then the journal can charge other academics huge sums of money to read your work and you will see none of this money. And additionally, you may no longer even be permitted to even put the work up on your own personal website. In my opinion, this is a terrible practice, and flies in the face of academic tradition. It makes it really hard for people like me, a person who doesn't have expensive journals paid for by their academic institution, to read your work at all.
I would ask for details, and demand that your work be published in an open access journal. But, of course, maybe you don't care, or think that plebs shouldn't be allowed to read your work. I have my opinion on this, obviously, but yours may be different, and hopefully this answer helps you understand your options even if you don't want to do things the way I suggest.
Another test is to see how they respond to the idea that you will put the paper up on a web site with a creative commons attribution required, derivatives allow, no commercial profiting without your permission sort of license. There you are very explicitly allowing derivative works.