Is it possible that the summons available to the summoner are different from those you may fight through storyline or otherwise? Maybe you will be able to fight Garuda, Shiva, Ifrit, Ramuh, and Titan for quests or loot and summoners will be able to summon Odin, Bahamut, Leviathan, Carbuncle, and Phoenix that way there is no overlap between what is seen or interacted with in the world/quests and what summoners are able to control.