Rainbow Servant doesn't work that way. What it does is add all the cleric's spells to your arcane list. It does NOT make you a divine spellcaster in any way, shape, or form. For all effects and purposes, the line "spells count as divine if not from the Cleric/Wizard/Bard lists" doesn't make you a divine spellcaster because you're still using arcane spell slots to cast them.
Clean and simple.