You are correct. Snivy also does not learn Leaf Storm through egg moves.
Though the majority of all Smogon LC players use simulators such as Pokemon Showdown and Pokemon Online which lets you build a team. The Pokemon may use any moveset as long as it is legal. That said it does not take into account the level, therefore you may use moves like Leaf Storm at lv5.
Most people that use wifi competitively use methods such as Pokegen to create their Pokemon. This means the Pokemon can be any level, with any ability and moves. This is done so that the Pokemon has access to moves like Leaf Storm as well as full evs and ivs.
So Smogon makes the sets in mind of those who use methods such as the above as otherwise in game you have a very small chance of getting a Pokemon with full ivs, evs in a short period of time.