I don’t think there is a problem in engineering, because of the high demand for Ph.D. engineering outside of university research, coupled with the intent of people pursuing Ph.D.s to go outside of academia once they graduate, from the get-go, as several people have mentioned above.
The authors of the report would have done better to look at theoretical physics, if they wanted to show an academic market mismatch. Many of the people doing Ph.D.s in theoretical physics are interested in academic careers, at least at the outset. A few of them will be interested in teaching in colleges without Ph.D. programs, so they will wind up in academia without counting against the “replacement” number for their Ph.D. advisor. I suspect that most of the theoretical physics Ph.D.s do find employment in their fields, in industry or government labs, if not in academe. Some go into finance. (Now, some start a theoretical physics Ph.D. with the intention of subsequently going into finance.) But friends report that small fractions of the set of Ph.D. candidates who originally wanted to have a university research career actually got one. This is happening, despite the fact that theoretical physicists are not exactly prolific in producing newly-minted Ph.D.s
I believe that there is also a problem in the life/health sciences, in fields where research is supported by the National Institutes of Health. From editorials and articles in Science, this has become a serious concern. In these areas, the research group sizes tend to be much larger than in physics (overall, could vary from institution to institution), and so there are many more people looking for academic jobs than the replacement level.
The point about hiring coming in waves is a valid one. However, I would view claims that there would be high demand for Ph.D.s in academia with some skepticism, if I were embarking on an academic career now. It used to be claimed that there would be many openings in academia once the people who were hired in the late 1960’s started to retire. Most of those faculty members have retired by now. Although academic hiring did ease up a bit, the projected high demand did not materialize.
If one is counting on the retirement of baby boomers to create large numbers of job openings in academia, I think one will be disappointed. Academic hiring was at a low level when the baby boomers entered the university job market. I recall one of my faculty colleagues saying that there were exactly 7 openings at Ph.D.-granting institutions in his field when he entered the market. And by his “field,” he meant about 1/6 to 1/5 of all of the faculty positions within departments, not his research specialization.