I'm certain that by the letter of the rules all of this is correct, but I'm not sure it's the intent of it.
Why be so specific to refer to it being considered 'on the caster's spell list'?
Why be so specific to point out that it is from the cleric spell list when there are arcane casters with the full range of cures on their lists (I think. Witches do, right? I could be wrong here).
Why write the fluff referencing divine power specifically?
'A white mage is an arcanist touched by a divine power and gifted with the ability to heal others.'
It just points to a more nuanced intent than the RAW approach would indicate.