The advantage could come if you trained lefties to work with righties in pairs or lines during melee. You could work with partners on either side for combined defense or offense. Biblical era combat was not well known for that sort of extraordinairy discipline, however, so it seems like a 'Well, it seems true' kind of story.

Anyway, in this particular story it talks about men using slings with their left hands. Changing the angle of attack with that type of ranged weapon could very likely increase it's effectiveness because most opponents would be carrying a shield on the other side, thus making it harder to block missiles across their body. I imagine storming a gate would be a situation where the advantage of the left handed slingers is cumulative, allowing them to open a wedge or gap in the enemy's concentrated defensive formation more rapidly than right handers.

It all sounds rather apocryphal, however, keeping in mind that it was always in a nation or army's best interest to make their tactics sound extremely effective no matter what their actual results on the field.