When a hiring manager specifically excludes overqualified people, this is a pretty big red flag to me. Managers usually only say this when they have a very tedious or low paying job that they think a PhD-type will quickly abandon for something better. I wouldn't exactly call this a "closed door", I'd say it's more of a sign that there are lots of better opportunities for qualified people. If these other opportunities went away, then the tedious jobs would start raising their qualifications too.
PhDs also have many other "open doors" that other people just don't have. All those teaching and research jobs you mention are available to them.
One can only hope (but I doubt it). Google doesn't hire just any Ph.D. -- they hire the best people who have CS experience, and that's only a tiny sliver of the total Ph.D. pool.
That said, I've experienced the downside of the degree, particularly when interacting with tech people. Lots of geeks get their dander up when they find out you have a doctorate, and start hammering on you harder, as if to prove something to themselves. I've also had people explicitly question my interest in jobs, to my face. It's definitely a real phenomenon, and I can understand why people might want to remove it from their resume. (If only it were easy to explain that 5+ year gap in employment history....)
I've had this happen as well, but once you overcome these obstacles, you are at an advantage.
On interviews, I get that initial skepticism that I'm too "pie in the sky". That vanishes after a coding test. As for my interest in jobs, I've been asked that, but it's always been a fair question (in fact, I've never been asked that about a job I really wanted).
I'm just saying that I've personally experienced the downside, so I know it's not a made-up phenomenon.