Eh... I'm not sure if I'm understanding the discussion properly, but the short version of this is:
Extra Spell would add an additional spell known. That spell must be one that the wizard can cast; i.e., the Wizard couldn't take Flame Strike, because Flame Strike is Divine, and not Arcane. Can you burn the Feat to create a new spell? Sure, but that's DMO and not how the Feat was originally structured.
The trusty SRD has this to say:
Quoted from the SRD
Spells of the prohibited school or schools are not available to the wizard, and she can’t even cast such spells from scrolls or fire them from wands. She may not change either her specialization or her prohibited schools later.
We also know that a Wizard can learn an unlimited number of spells; if the Feat reads as you say, that it allows a Wizard to research a spell she would not otherwise learn, then I would have to assume (without reading the Feat myself) that the wizard can, in fact, learn a spell from a banned school. Otherwise you're just taking any spell you could get in a much simpler way and blowing a feat for it, which is a perilously high cost considering the return.
Oh, and research is, quite obviously:
Quoted From the SRD
Wizards perform a certain amount of spell research between adventures. Each time a character attains a new wizard level, she gains two spells of her choice to add to her spellbook.
Independent Research: A wizard also can research a spell independently, duplicating an existing spell or creating an entirely new one.
And, don't forget that all new spells must be DM approved. So in terms of how research works, this would be what the Feat is referring too. The SRD is extremely specific about there being no way to gain a spell from a prohibited school, but I would yield that if a Paladin can take a feat which allows them to take an additional class without losing Paladin status, then a Wizard should be able to take a Feat that allows them to learn a prohibited spell.
LCpt. Thia Halmades