A full-list spontaneous arcane caster (Warmage, Beguiler or Dread Necromancer) does not pick spells to learn each level, like a Wizard or a Sorcerer, and cannot copy spells from other sources to a spellbook like a Wizard can. Their spellcasting instead functions very similar to each other, I'll use the Beguiler as an example:
Spells: A beguiler casts arcane spells, which are drawn from the beguiler spell list on page 11. When you gain access to a new level of spells, you automatically know all the spells for that level on the beguiler's spell list. You can cast any spell you know without preparing it ahead of time. Essentially, your spell list is the same as your spells known list. You also have the option of adding to your existing spell list through your advanced learning class feature (see below) as you increase in level.
A beguiler need not prepare spells in advance. You can cast any spell you know at any time, assuming you have not yet used up your spells per day for that spell level.
The Advanced Learning class feature mentioned in the text looks like this:
Advanced Learning (Ex): At 3rd level, you can add a new spell to your list, representing the result of personal study and experimentation. The spell must be a sorcerer/wizard spell of the enchantment or illusion school and of a level no higher than that of the highest-level spell you already know. Once a new spell is selected, it is forever added to your spell list and can be cast just like any other spell on your list.
You gain another new spell at 7th, 11th, 15th, and 19th level.
A Rainbow Servant gets the following feature:
Cleric Spell Access: A 10th-level rainbow servant can learn and cast spells from the cleric list, even if they don't appear on the lists of any spellcasting class he has. Such spells are cast as divine spells if they don't appear on the sorcerer/wizard or bard spell lists. This class feature grants access to the spells, but not extra spells per day. The 10th-level rainbow servant can likewise read scrolls with cleric spells on them and use wands and staffs that contain cleric spells.
It seems to me that Rainbow Servant is written with Wizard, Sorcerer and Bard in mind, all arcane caster classes that learn new spells each level. So:
How does this prestige class interact with full-list spontaneous casters, who have no per-level mechanic for "learning" new spells?
Does Rainbow Servant allow them to automatically know and be able to cast all cleric spells?
If not, are they limited to the Advanced Learning feature to "add" cleric spells to their list, or are there other ways?
Or does not even the Advanced Learning feature allow them to take advantage of the Cleric Spell Access feature, since it uses the word "add" and not "learn"?