When the ignition is turned off, power is cut to the computer, power is cut to the fuel injectors and power to the fuel pump is cut.
It cannot be Dieseling. with a lack of fuel because the PCM in not able to open any injector.
Exhaust can carry on for a few minutes after the engine stops due to shrinking by cooling when expansion is the greatest...

Is this true if one or more of the injectors are leaking? If they are leaking, they could at least leak gas into the cylinders until the fuel pressure subsides?

That could be true.
He does not state any other issues that should be present from leaking injector/s.or leaking anything.
A test of fuel pressure should detect leaking injectors as soon as the engine is turned off by observing a 'fast leak down' of pressure..
That could be a pump check valve or an injector. A leaking check valve would not cause Dieseling. The fuel pressure would just leak off back to the tank.
If the regulator is leaking through the vacuum line, the long term fuel tables should show a negative shift in reading to the Lean side from excess fuel while driving.. The Ox sensors detect this and cause the PCM to make the shift.
This issue has to be diagnosed without guessing..
In a carburetor engine, the fuel was just drawn out of the carb with no limitation until the combustion chamber cooled enough.
Sometimes that could be several minutes depending on how hot and chamber deposits conditions.

Bluegrass, as always, your knowledge and experience is appreciated.