90% baloney as usual. There are two ways to "run" an engine without a load on the ignition coil.
One is to hand start the engine with the spark plug wire disconnected. That won't do any damage as there's not enough energy in the spark from hand cranking to do any damage.
The other way is to run the engine for a while, and remove the spark plug wire. Assuming you can do this without getting a nasty shock, it might internally arc across the coil. However, in my limited experience with chain saws and small generator engines, a shorted coil will still generate a small arc. Not a hot or big as a normal coil, but unless the short is somehow across the entire coil (easily found with an ohmmeter test), you'll still see a tiny spark. Buy a real tester:
(I made my own spark gap from a piece of U shaped plastic).
What I think happened here is that someone transplanted the story from their automobile or multi-cylinder engine experience. With more than one cyclinder, it is possible to run the engine with one spark plug wire disconnected, which might cause internal arcing. However, it's not likely with a single cylinder engine.
Note that the coil part number that I excavated is used in Husqvarna, Tecumseh, Toro, and others. If it was as failure prone when NOT running as you imply, there would be recalls and other failures in epidemic numbers.
Testing the ignition:
This one covers most ways to test your engine spark.