In other FF, the white mage was a divine caster, powers from gods. FF14 WHM is a druid. No really, a druid. The source of the conjurer's spell is the elemental and nature. The WHM is one blessed by the elements.
Here:
Conjury calls upon the elements of earth, wind, and water and concentrates them to a potency at which spells can be weaved. Through practiced meditation on the essences of creation, conjurers draw forth and absorb aether from their immediate surroundings.
From:
http://na.finalfantasyxiv.com/about/...magic/conjurer
The WHM, from what I remember from the job quests, are the chosen of the elements.
So in short the whole dia thing doesn't work for them this round. They are not priests, they are druids and elementalist. Yippy lore! As for the ancient magic, I'm sure they can add another job to the conjurer to have them.