Salt does permeate the shell and flavor the egg, but not the quantities you're talking about.
How do I know? I grew up eating Chinese tea eggs, which are made by soaking a hard boiled egg in a salty solution. They're normally cracked but not peeled before soaking, and are soaked for a number of hours, up to a few days. Over the years, we've accidentally made some without cracking, and after soaking, they weren't as salty, but they clearly had a salt flavor.
For a quick boil like this, I'm sure the flavor impact is minimal. Salt has other properties, like raising the boiling point of water and pulling moisture out of solids via osmosis.
It's possible that one of these side effects positively affect the peeling or how the egg cooks. Perhaps someone came up with this technique with one of those parameters in mind, but the goal was lost in translation.
It could also be, as Sobachatina said, just a myth. It's not for the flavor, though.