Also that healing magic is divine only. Arcane casters are never allowed to have actual healing spells.
To say that healing magic is divine only, not arcane is a distinction you can only draw by looking at the spell lists. You can't tell from reading the rules for the spells.
This is what I mean when I question whether the distinction is even real in D&D. Spells all work exactly the same way. It is purely cosmetics whether they are divine or arcane. There is not even a written rule stating that all healing magic must be divine because arcane magic can't do that effect. there is no reason an AD&D Magic User couldn't create a new healing spell with the mechanics of the Clerical Cure Light Wounds spell, except Dungeon Master fiat saying "No, you can't do that." Nothing in the rules would prohibit it.