Just because magic has rules, that does not mean those rules are compatible with nature's rules. The conceit of most stories involving magic is specifically that magic is what is used to go against or even break nature's rules.
If it is within the universe, it is within nature's rules, because nature is the universe. It's just another word for the same thing. The laws of nature are not absolute; how they manifest depends on the specific conditions that apply. The way time and space behave deep in a black hole's gravity well seem to break the rules of nature as we know them, but that's because we understand those rules as they apply in more ordinary conditions. The way subatomic particles behave on a quantum level seems to break every rule of matter and causality and nature as we know it, but that's because what we know is the particular subset of rules that apply on a macroscopic scale. In a universe that includes magic, then magic is part of its rules -- just a part that's distinct from the more familiar, everyday rules we're used to. But if science could expand to encompass those seemingly "rule-breaking" phenomena that happen at the quantum level or in extreme gravitational conditions, then it could expand to encompass the "rule-breaking" phenomena that happen when magic is involved. Learning new sets of rules is something science has been doing quite successfully for hundreds of years now.
And seriously -- no depiction of magic in any fiction I've read is anywhere near as bizarre or defiant of conventional logic as quantum physics is. And yet quantum physics does follow a very structured set of rules that we have deduced and learned to work with. There's a difference between breaking the rules we know and following no rules at all. It's pure arrogance and ego to assume that the limits on what we currently know are absolute limits on reality.
You're arguing that because it "exists", science can be extended to it, but the whole point of having a different name for it in fictional stories is to stress that science can't be extended to it, and that it exist outside of the realm of "regular" rules which govern the universe.
Yes, I know that's the common premise in a lot of stories, but my point is that it's a deeply ignorant and wrongheaded premise, because it fundamentally misunderstands what science is and how it works. The assumption that science cannot be extended to something beyond its current limits is a contradiction in terms, because that is the whole purpose of science. So yes, obviously I know that a lot of stories make that assumption. What I'm saying is that I don't buy it for a second, any more than I'd buy the premise of a story that said humans and dinosaurs lived together or that men are smarter than women.