I think the truth is somewhere in the middle, with the anecdotes about GS' hatred (and lack of) fitness training come from earlier on in his career in his 'dred' phase when he was a little chubbier. Even towards the end of his time in Aus (2007-9) you'd notice his body shape changed substantially, a conscious decision coinciding with a bit of a loss of pace no doubt (as happens to most players mid-career).
Obviously, as many have said, explosiveness, decision making on 'when/where' to pilfer, and fearlessness, are key attributes for opensiders at the pilfer, but fitness is the underlying trait that gets you the opportunities to practise all of the above. When you're a young bloke that fitness and mobility around the park just comes a little easier.
There's a reason the 7 and 9 are 2/3 of the players that cover the most metres in a game, and that's because they have to get to the most breakdowns. Fitness is key.
Correct me if I'm wrong, I was young in his peak, I remember GS as a player that's dynamism as a link man was always more valuable than his breakdown presence.