I would like to hear some stories, and studies on this topic.
We've all seen the various ad's in the past of an engine running with out oil. I have also read some stories from aviators that had engines run out of oil, and the engine was saved from damage. I can even think back as a youngin when a friends vehicle ran low on oil and siezed the engine, rather than figure out how to tow it back home, I bought some oil, put it in, and of course the starter wouldn't budge it so I told him we will have to coast it to 35 and pop it into gear, it was a automatic. It started and was fine. I don't remember how long he drove it after that, and it may have ran low a few other times too and done the same thing.
I know very well what happens with no oil delivery to the bearings, I have had to repair many such failed engines.
Like a diesel engine that ran at idle for maybe 15 to 20 minutes before it seized.  
How long can an engine run with little to no oil delivery and low power before bearing damage occurs?
I know of a fellow that ran a big radial engine mistakingly with very low oil level, its a dry sump, and 4 gallons maybe in the whole system if even that much I think it is meant to hold 20 or 30 gallons, it showed cranking oil pressure, and ran maybe 2 to 3 minutes, he doesn't remember checking oil pressure after it was running after initial start. My first guess is there was not even enough oil to scavenge any debris if there was any. So inspection of the filter would be worthless. The oil used is close to SAE 60. 

I once had a motor scooter that after an overhaul was real tight would seize up when it got hot and I'd just have to sit on the curb and wait for it to cool off.  When it did, I could crank it and drive it until it seized up again (which it did often until it got good and broke in.  So excessive expansion of internal parts might be the culprit with seizing up rather than actual engine failure.  That scooter went on to run for many years once it loosened up real good.

Other than that, low lubrication and no lubrication are two entirely different things.  Lubricant capacity has an element of cooling involved as it sits in the 'storage' phase, so with low storage amounts, the danger is overheating of the lubricant, which the engine doesn't necessarily care about as long as something lubricates it, but the oil properties (additive depletion and viscosity indexer destruction) might.  So an engine might run a long time with low amounts of oil and the only result would be trashed oil rather than a trashed engine, unless of course you operated it until the complete failure of the oil led to the complete failure of the engine.

These anecdotal tests where someone drops the oil out of an engine and runs it for "X" amount of time... well, let's just say I am from Missouri about all that.  Without having seen what was really in there, or what was in there before the "miracle oil" was put in and then drained, well, I'd have to have lots more knowledge about the controls applied to such a test.  Not that I don't believe the results, necessarily.

I have a personal experience to relate.  In 1984, my Father in-law bought a used 1982 Toyota pickup with the 22R engine in it.  It had about 20K miles at the time.  From the day he bought it, the oil pressure warning light would take about 10-20 seconds to go off after you started the engine.

Over time, it got worse and worse.  I was always after him to check it out, but he is totally non-technical and didn't seem to care.  When it was taking a minute or two for it to go off, I told him it wouldn't be long for that engine to be toasted.  In 1989, the light finally wouldn't go off at all, and it started to knock.  It had 75K miles at the time. I bought it from him for $100.   I drove it 500 miles from his house to mine & the whole time the oil pressure light was on that whole distance.  When I pulled into my driveway, it was rattling pretty loudly.

I bought a 22R from a wrecked pickup that had about 80K miles.  It had a different oil pan (4WD, mine was 2WD) so I had to take the pan off the trashed engine.  When I pulled the pan and the oil pickup tube and screen, I immediately saw why it had no oil pressure.  The oil pickup tube had a manufacturing defect, a large blob of weld on the flange where it met the flange on the block, and the gasket was gone around the blob of weld.  It was sucking air from day one, and eventually quit pumping at all when the gasket fell away.  I pulled a couple rod bearing caps for grins.  The bearings were really worn, but weren't spun out.  Cylinders didn't look too bad.  Probably had enough splash to keep the cylinders in good shape, but the bearings suffered from little to no pressure.

I eventually sold that truck with 375K miles on that replacement engine.  It still ran great, but the frame was rusted out....

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