There are three types of jobs a PhD could go into: A) industry job (just job to us mortals), B) industrial research lab (a company, but does research. An example would be IBM or Microsoft Research in CS), or C) a professor. For context, I work in a research group in a building full of PhDs, postdocs and professors.
For A, PhDs ought never be short of work. They were likely good students, they also spent 3-5 years looking at the state of the art in their field. Something should've rubbed off along the way. So a PhD is usually a good signal (but many smart people decide not to do PhDs, as well).
For B - the supply of places which will pay you to do actual research rather than company-specific goal stuff is much reduced compared to the supply of PhDs. This is why you'll find plenty of PhDs at Google doing software engineering - sure they're PhDs and they're smart, but they're likely not still publishing much. Whereas MSR/IBM research groups do publish (and in many ways act like a university).
For C - the chances of getting to tenure-track professorship are low, and when people say there aren't enough jobs for PhDs this is generally what they mean: there aren't enough academic jobs. The usual process is to become a postdoc and then to become junior faculty - a professor, but not tenured. Then you must seek promotion into a tenured role. Sometimes people skip steps, but this is the path people I've talked to have taken. Each stage is competitive: you have to convince a professor to take you on as a postdoc, then you must convince hiring committees you should become faculty and that you have the potential to become tenured. All the while, you must deliver enough research output to back that up.
At each of those stages, there's a relatively high attrition rate, and this is amongst people who obtained PhDs.