A young man with no military experience vs. a giant who's killed every soldier in the army who's attempted to fight him qualifies as an underdog story in my book. Also I'd assume archery skill doesn't really transfer very much to using a sling
Some scholars believe that Goliath suffered from a genetic disorder that may have left him rather "simple" in intellect. And slingers during that era were vicious killers capable of hitting birds in flight along with other examples of their prodigious skills and lethality.
The segment made the case that David vs Goliath was a stone-cold killer against a relative 'innocent,' it just happened to be David who had the distinct advantage.