Gaia is the planet, with its own set of rules which must be conformed to if an outside element is brought to it. The Throne of Heroes is a realm outside of it, where humanity's legendary heroes are brought upon their deaths. It is perhaps the best example of how rules are absolute in each individual realm.

[He looks pleased. He does, at least, appreciate intelligence]

Precisely. Power means nothing if a particular feat is, in essence, impossible. Either these 'gods' possess power to circumvent those rules -- highly unlikely as they have summoned us to perform a task they cannot solve themselves -- or they are pretenders who have acquired some skill which overrides the physical rules of all possible realms.