That's a description of tracing GC, not a definition of GC.
GC is whatever technology that enables what you've called automatic memory management: a kind of illusion that there is infinite memory, from the programmer's perspective.
That might involve some mix of reference counting (Python is probably the biggest example), tracing (what you seem to think is all of GC), data flow analysis (e.g. escape analysis in some Java GC / JIT integration), etc.
That's definitely not what McCarthy meant by it. I understand that's probably a common view nontheless, but I can use sbrk() and the fact my computer has gobs of ram/swap, and I'm not going to call that garbage collection. I don't think this definition is useful.
If you re-read what I wrote now understanding what I mean when I say "garbage collection", perhaps we can talk about strategies for providing that infinite view of memory instead.
To seriously tell people that every C program running on unix has automatic "garbage collection" built-in seems like it would create very confusing conversations.
This is demonstrably not true. The Garbage Collection book by Jones is the key text in this area, and it covers reference counting under that term. It was published in 1996, before Hacker News existed.
There is also Bacon's Unified Theory of Garbage Collection, 2004, which said the two are on a spectrum that meets in the middle.
> all high-performance collectors (for example, deferred reference counting and generational collection) are in fact hybrids of tracing and reference counting
Garbage collection is about visiting live objects to figure out what's alive and ignoring the dead stuff. Every theory about why GC can work (or be useful) is predicated on the idea that there is more garbage than live objects so you're touching less stuff.
If all you do is mark/sweep, you're visiting the garbage as well, so GC research has led neatly into moving collectors (which don't ever touch the garbage). That's a win, and that's why GC is worth study.
There are other kinds of "automatic memory management" though: reference counting, arena allocators (at a stretch), and object memory (I've only seen this on mainframes), and they're all worth some attention.