I had a set of Araya wheels with narrow (700c x20) hooked rims and high pressure (150psi max) Continental clincher tires.
I installed them on a road bike, and took a test ride. I did not get far and the tire started to roll off the rear rim.

Remarkably, I was able to remove the tire without any tools (normally I can't do this). I inspected and no problems were apparent. I assumed it had been under-inflated.
Then I reinstalled it, reinflated to 140PSI, and took a second ride....

I started out OK, but then the inner tube blew with a loud "pop", and wrapped itself around my rear brake and axle.

I walked back, untangled the inner tube, and indexing the torn section to the presta valve hole, I checked for any bit of glass: None found -but THIS time, I noticed a slight low spot in the hooked rim - one not immediately apparent to the eye, but one you can most certainly FEEL.

On consideration, I suspect THIS was the reason for the blow-out - though I have NEVER experienced such a thing with any other tire!
(Even cheap, six-dollar 27x1" tires from Niagara will stay on with a big-old-huge-honking dent in an unhooked rim.)

So what I need to know is this:

Is it because all skinny high pressure tires are immeasurably more sensitive to such things?
- or is it because CONTINENTAL high pressure tires are more sensitive to such things?

140 psi is high, if you rim is defective, you say it has a low spot, guess it is possible that this damage / low spot was enough to let the tire roll off. have you tried tunning between 90-110 psi, as this is more normal. Was the tire installed correctly in the first place?

Visually the tire was seated - at least before my second ride.
I have to agree with you that 140 (even with a 150 stated max) is high. Still I've never had a tire blow off when I was within the stated limits.
( I am hearing myself talk and convincing myself that the Continental tires are at fault. This is just not normal for other brands.)

My experience has been faulty technique, by me. Sometimes I get lazy and use an air compressor to inflate the tire. I am always better off using a floor pump, and inspecting the bead during the inflation (and making sure tube is not pinched). I've had about a half dozen roll off, every time, I used the air compressor to inflate.

The verdict:
It was the fault of the Continental tires.

I installed another brand of tires and whilst putting them on, I could tell immediately that they were going to stay on.

I took a test ride and cornered at speed, with no compunctions about it whatsoever - the replacements were that much more confidence-inspiring.

The replacements ride better too, whereas the Continental Grand Prix's that I removed felt squirmy and rock hard at the same time.
- FWIW, they looked good on the bike. (below) The replacements are black walls and not so classy looking.

Keep in mind that half of the tire/rim interface is the rim. It doesn't matter what the rateing for the tire is if you're exceeding the capability of the rim.

27 inch rim tells me that it's pretty old. What does the brakeing surface feel like. If you can feel a noticeable concavity, your rim is on it's last legs. As the brakeing surface of a rim wears it makes it easier for air pressure inside the tire to push the rim flanges outward. When that happens, it's easier for the tire to blow off.

So, what's the max pressure rating for your rim?

If you exceeded that, it ain't the tire's fault.

While rims can crack if the pressure stress is greater than what the flange can take, they don't ever flex far enough to shed a tire.

To my knowledge rims are not pressure rated, but they are designed to mate best with tires in a width range. I've seen large section high pressure tires crack rim flanges, but only after there's been some wear. Other than cracking or being undersized, I can't imagine a rim as the cause of a blowout.

There could be a tolerance issue with a particular tire & rim if the tire is at the high end of the size band and the rim at the low end, but more likely the blowout was caused by the tire's not being perfectly seated, or the tube being trapped under the bead when mounted.

Also, some tires do better with hook edge rims and others with straight side rims. Unfortunately, makers don't make it clear in their literature.

I don't know what the rim's max pressure allowed is, but the rim was a top-of-the-line 700c red label Araya from the 80's.

I am sure that there was no inner tube hung up, because I had just got done having teh tire come flailing off on my first test run and I was a little nervous about it.)

- If it happened in the front instead of the rear, it would most certainly have rearranged my face.
- When a tire lets go like that at speed, wraps itself around the brake caliper and stops the bike dead, then there is only one place the rider can go.