My copy of the Jones/Lins Garbage Collection book I'm looking at on my shelf makes this quite explicit, the chapter on reference counting makes it clear it's one form of garbage collection.
When I was messing with this stuff 20 years ago, that was my understanding of it, anyways.
There are advantages and disadvantages to reference counting. I think some of the confusion in terminology and some of the frustrations (or opposite) here comes from the rather awkward way that Objective-C implements reference counting as something you have to be explicitly aware of and careful about, even with ARC. My brief stint doing iOS dev made this clear to me.
But I've used (and written) programming languages that had transparent automatic garbage collection via reference counting, and the programmer need not be aware of it at all, esp if you have cycle detection & collection (or alternatively, no cycles at all). And, there are compelling RC implementation that are capable of collecting cycles just fine (albeit through a limited local trace.)
Anyways, he's right that RC can be better for things like database handles etc. Back in the day I/we used reference counting for persistent MUDs/MOOs, where the reference counts were tracked to disk and back, 'twas nice and slick.