Consider this. The link between an eidolon and summoner means that an eidolon can touch those protected by spells such as Protection from Evil/Law/etc. Also, when an eidolon is knocked to negative hit points it doesn't automatically vanish back to it's other-dimensional home, it stays until it reach its negative CON. Also, a summoner can give his hit points to him eidolon under certain conditions and vice versa.
This would seem to indicate to me that eidolons are very similar to your regular party members who benefit from Cure wound spells. The Rejuvenate Eidolon spells seem to be some variant that summons other-dimensional energy from the eidolon's home realm, or perhaps something even more esoteric and heals the eidolon. In the case of my summoner, I could say I'm pulling more life from the slumbering primordial being that my eidolon is a mere shard of, but nobody really cares where it comes from in my game.
Also, I know I've been frustrated in combat when we are doing damage to a demon and then it pulls out a potion, drinks it, and gets healed. Not only is it using our soon to be treasure, we have to do all that damage again.