Sure it does. "Paladin Spells" are defined on PHB pg. 191.
Even an Archivist can take the feat, simply because they can learn these exact same spells. (The feat will only apply to these spells.)
If <Class> Spells is seriously just shorthand for "Spells found on a given class's spell list" (This seems too sensical for WotC circa 1999), then im pretty sure every class in the game can take Battle blessing, As a result of i dont think a single class that gets vancian based casting doesnt have read magic as a spell.
Although it looks more like you have to actually be able to cast the specific spell list, as the term seems to actually be referring to not just spells castable by the class, but the specific setup of spells which make up that list.