Pretty much. They are gods that even the beastmen worship and wouldn't even think about messing with. You know, those beastmen who are an actual threat to us because they possess comparable power and numbers. They are gods who control the elements. Now it should be noted that it appears that Leviathan does some of the Sahagin's bidding but likely only because they worship him and of course complete the necessary ritual to summon him for short periods of time. This is more apparent in the 3rd Limsa story quest though one could also say it was merely a coincidence that Leviathan appeared and attacked you, he could be attacking you of his own will.
Aion however actually had an interesting system. Instead of summoning a god you summoned an elemental spirit. As you leveled up you got higher ranks of the summoning spell which allowed you to call forth larger and more powerful variations of that elemental spirit. However people wouldn't be happy with anything remotely similar for XIV as anything short of all the classic summons would bring about a riot.