There is no such thing as the class spell list for spells for the fighter's potential weapons 'known'.
There is a direct analogy between a class' spell list and a class' list of proficient weapons, and both lists expand in virtually every new book. Each is a list of tools for the class described.
Some classes lists are defined by "Simple/Martial/Exotic" proficiency, while others have ennumerated lists of proficient weapons- an analogy conceptually no different from full casters and classes like Bards or Rangers with limited spell lists.
Similarly, Extra Spell adds one spell to a spellcaster's known spells- he can cast it.
That's an assumption you make, that is not only not supported by the rules, it's actually outright contradicted.
Extra Spell's text starts off with:
"You learn one additonal spell at any level up to one lower thatn the highest level of spell you can currently cast."
According to p.179 of the PHB:
"A wizard can also add a spell to her book whenever she encounters one on a magic scroll or in another wizards' spellbook. No matter what the spell's source, the wizard must first decipher the magical writing...Next, she must spend a day studying the spell. At the end of the day, she must make a Spellcraft check...If the check succeeds, the wizard understands the spell and can copy it into her spellbook...A wizard can also research a spell independcntly, duplicating an existing spell or creating an entirely new one."
I don't see a contradiction here. A spell "learned" has been deciphered and transcribed into the wizard's spellbook, and such a spell is memorizable and castable as long as the wizard is of sufficient level.
Theoretically, a Wizard could transfer any arcane spell transferred to scroll or book into his own, regardless of class lists, given sufficient time and research money.
Extra Spell just cuts through the game mechanics of learning by having the PC burn a feat.
If a wizard could only cast spells from the extant sorc/wiz list (how many ever books you're using to define it), then independent research would be impossible- such a spell would- by
definition- not be on the class list.