Guys read the quote and the spell section for the Beguiler and the Warmage again. I believe that the intention behind the quote was to allow whatever Advanced Learning spell chosen appear on the spell list, and only that. Unfortunately the logic and the language of the quote are unmistakable, if Warmage or a Beguiler knows a spell it is on their spell list.
Again, do I think the designers intended this? No
Do, I think it is a good thing? No, not really
Do I think the language and logical implications of “Essentially, your spell list is the same as your spells know list" is plainly written and intelligible? Yes.
Alas there is a reason why people take great care in crafting legal contracts, and generally do not put in descriptive text, as that often leads to unintentional consequences.
Logically again it follows that, assuming a strict interpretation of the rules:
A) You can use Extra Spell to learn a spell not on your class spell
List.
B) Under most circumstances knowing a spell, is not sufficient to
Cast it; the spell must also appear on your class spell list.
C) The Warmage, Beguiler, and Dread Necromancer cast spells
Like a sorcerer, and know all of the spells on their class spell
list. The above 3 classes can also add new spells to their their
spells know and to their class spell list via the Advanced
Learning feature.
D) The Warmage and Beguiler both have a specific line that says
Essentially, their spells known and class spell list are
analagous.
Without going into syntaxatical discussion of the true meaning of what " Essentially" means in the quoted line, I think the logic is decent.
What it also shows to me, is this in not a question that can be solved by a strict inteperatation of the Rules As Written. The Rules as Written here blow.
The easiest solution is of course to rewrite the Extra spell feat, and not all the pre exsisting rules. The debate, in my opinion needs to be: would it be unbalancing to have Extra Spell add spells to a personalized class spell list, and would it be unbalancing for an Arcane caster to add Divine spells and vice versa?