As a concept, you simply say that "divine power" is a cosmological entity related to, but not originating from, the gods.
In the Forgotten Realms, for example, the fact that various divine "portfolios" are movable and capturable between deities certainly strongly implies that the power is not native to the god.
And while I know the Realms has had gods act as gatekeepers to the power in the past, the change present in the DMG would imply that there may be a retcon or change. (Or maybe not! WotC isn't a stickler for lore coherence.)