Most UX methods and guidelines come from HCI (and HCI, of course, comes from other disciplines).
Is knowing some HCI useful for design? Sure, but necessary? The best designers I've worked with have none, while going from HCI to design requires a drastic shift in mindset. Keep in mind that HCI first and foremost is a computer science discipline practiced exclusively by computer scientists. Design is mostly practiced by those trained as designers, in design school by people who have never been remotely near HCI. They are definitely analytic, but are not data driven (well, google, and in the web world where engineers have taken over, but that's a new trend and not necessarily a lasting one), their method is design thinking rather than the scientific method.
Most work on HCI was at the measure level. If you follow HCI research, you may notice a trend: lots of publications based on ethnographic methods, qualitative approaches and the like. HCI (as in "HCI academic research") is, nowadays, much closer (methodologically) to design thinking than to experimental psychology.
> I'm betting you are on the HCI side and not the design side right?
I do both. I work in the industry (UI design, front-end dev, evaluation) and I'm a PhD student.
> Keep in mind that HCI first and foremost is a computer science discipline
I've the opposite opinion on this. From all the disciplines that "inform" HCI, CS would be the least important. But ...
> practiced exclusively by computer scientists.
I guess you're right on this, at least in the academia. I do have the impression that most HCI researchers have a CS background. But, at least in my country, this is mostly because CS departments have much more funding to hire researchers than the others.
I don't think you can simplify it to HCI preceding UX or UCD methodologies.
As you point out, HCI of course comes from other disciplines and just like the field of UX, it's borrowed a lot. HCI, Human Factors, Psychology, etc., all borrow techniques from others (as you've acknowledged)and a lot of what they do has been developed in parallel.
A lot of UX and design methods were developed in parallel by designers with at traditional design background or others without formal research backgrounds. Despite UX being characterized as a science or more rigorous than traditional design, it is largely a pragmatic practice.