It's important to differentiate between the classic profiles (largely from the 1980s) and the modern ones (typically Chinese).
The classic MX profiles largely come from Cherry (Cherry-profile!) and SP (DCS, DSA, DSS, and SA). The new profiles often are produced solely in China (MT3, KAT, ASA, SS2), even if some like MT3 were designed externally.
The reason I mention this is that a number of the popular classic profiles have actually been cloned by Chinese manufacturers, especially Cherry and SA-profile, and to a lesser extent DSA profile. This means that, yes, if you see SA, Cherry, or DSA keycaps not manufactured by Cherry or SP, then they are indeed "fake" "clones."
None of them are licensed. The DSA, SA, and Cherry out there are 'cloned' from measurements, either open-source information or just reverse-engineering the profiles. The closest thing to 'licensed' Cherry-profile are the CRP dye-sub keycaps. They seem to use tooling derived from original Cherry PBT tooling for PBT keycaps, so they are actually sort of authentic.
The largest variance in dimensions of clone keycaps is definitely in so-called "Cherry" profile. GMK is currently the standard and authentic "Cherry-profile." Many "Cherry-profile" clone sets don't match these dimensions. For example, ePBT is supposed to be Cherry-profile, but it seems to be about 1mm higher. Not fully compatible, then. Other cheap Cherry-profile, on AliExpress for example, may not be to spec. I find that these Cherry-profile 'clones' are the least reliable in terms of getting the dimensions you expect.
The SA-profile clones are often quite close in dimensions. They could probably be treated as true SA-profile sets, even though they are not from SP. I've seen a number of bargains on Chinese websites, and you can get decent-quality caps this way. DSA is a little more of a crapshoot, as I find that SP quality is significantly better - but the clones are often PBT, which is harder to work with.
I don't know about the legal issues involved. I think that Cherry, SA, DSA, etc... are out-of-copyright in terms of their dimensions, I don't think those profiles can be IP-restricted. However, use of trademarks like SA, Cherry, etc... is questionable, even though the clone manufacturers do it.
So to answer your question, those 1980s keycaps profiles were originally exclusive to certain manufacturers. However, they have been since cloned. The new (largely Chinese) profiles tend only to be produced by their originating manufacturer in China, partly because of copyright and IP agreements (as in MT3, which is exclusive to Drop), or because no other manufacturer wants to make expensive tooling to illegally copy someone else's new profile. So MT3, ASA are manufacturer-exclusive. ZDA seems to be an unlicensed clone of XDA profile, if I'm not mistaken.
Any MT3 that isn't from Drop is an unlicensed clone, as it's definitely a licensed IP, although the dimensions are public. I haven't heard of any clone sets of MT3. Not needed when the other Chinese manufacturers have ASA, MG and unlicensed SA.