Quote Originally Posted by Grim Reader View Post
There is no law saying that Rainbow Warsnake must work for the fixed-list casters.
No, just the rules saying that.

The fact that they do not pick spells known make them unable to take advantage of the Cleric spell access. Also the feature even specifies that the spells don't appear on his lists:
That says the character may "learn and cast spells". The mechanism by which a Warmage learns spells is "automatically". All the ways in which a Warmage learns spells function automatically. As a result, an ability that generically allows the character to learn spells from some new source automatically provides all of those spells unless it specifies its own rules. Your logic would allow us to prohibit any class from using the capstone, as it never specifies those classes use their normal mechanism either.

If the ability said something like "when the character gains a new level, they may select spells from the Cleric list as new spells known", you'd be right. However, that's not what it says, and you're not right.