Sorry, the information at that link, Cecil Adams, is not so much wrong as it is incomplete.
Running regular fuel in a HIGH compression engine designed for premium is a lot like running a TOO LEAN mixture in a low compression engine designed for regular fuel. Timing could be perfect, absolutely optimal, but the lean mixture would still oftentimes result in compression knock.
Back in the days of carburation the only option would have been to change the jets in the carb to get a richer mixture.
NO MORE…!
These days if the engine controlling ECU detects TDC(compression) knock/ping and the ignition is already optimized the ECU will simply enrich the mixture to alleviate the knock/ping.
Obviously this will also work with a high compression engine designed for high octane but presently fueled with low octane.
So the question becomes…
Will the use of the richer mixture to overcome knock/ping overcome the economic advantage gained by purchasing the cheaper low octane fuel?
NO.
Provided you are not of the teeny-bopper boy-racer mentality and therefore are often in the WOT parametric realm. Absent a FULL charge, or nearly so, in the cylinders there will be no issue of TDC compression knocking.
Which brings us nicely to the subject missed in the link.
Knock/ping due to engine lugging.
This is when the “back-load” on the piston is so high it cannot travel downward as fast as the flame front is expanding. Obviously any fuel, of any octane level can and will be subject to this and just as obviously ignition timing will play no part in this issue.
But.
Lower octane fuel (think diesel) contains more energy and therefore burns more “explosively”, more rapidly advancing flame front, and therein lies the problem.
Most modern day passenger vehicles have automatic transmissions so the controlling ECU executes a downshift if knock/ping is encountered in the parametric “region”.
With a manual/stick shift the only option, regardless of fuel octane in use, is to enrich the mixture slightly until the driver gets the “message”.