Sorry, but I don't think that's the case - overfilling it might cause problems (although no where near as bad us letting it run dry), but its far better to keep it topped up to the Max
Actually in petrols, its not so bad, but in modern high compression diesel common rail engines, over filling them can cause the oil to blow by the scraper rings and actually combust with the air/diesel mix... That is very dangerous, and very explosive!
Anywhere between and up to Max is perfectly acceptable. Filling it to max isnt dangerous, neither is a drop more (though it should be avoided!), its when you massively overfill it that it becomes an issue.
For example, an Peugeot HDi engine can 'run away' (where oil gets past the scraper rings and cause an unstoppable combustion) with as little as 0.5ltr too much of oil. It will effectively increase revs until the engine cannot take the stresses anymore and goes bang... Ive seen it happen once, and it blew the whole front end of the car in question to pieces...