Where does it in the rules say that a Quarterstaff can be used as a Staff Implement?
Where does it say they can't?
Rule: p158 Wizard Implements "A wizard wielding a magic orb, staff, or wand can add its enhancement bonus to the attack rolls and the damage rolls of wizard powers"
Rule: p215 Weapon Groups "Weapon groups are families of weapons that share certain properties. They’re wielded similarly and are equally suited to certain kinds of attacks. In game terms, some powers and feats work only when you’re attacking with a weapon in a specific group."
Rule: p216 Definition of Staff Weapon Group "Staff: In its most basic form, a staff is a long piece of wood or some other substance, roughly the same
diameter along its whole length."
Rule: p218 Weapon Chart showing what weapon group a quarterstaff is in "Quarterstaff ... Staff"
So, RAW the wizard may use a staff as an implement, and a quarterstaff most definitely is a staff. Ergo, RAW, they can use a Quarterstaff as an implement (or a Long Staff, Bo Staff, Three Piece Staff, or whatever other types of Staff may eventually be produced).
RAI? Hoo boy, I'll make no bets. Especially not after a WotC staffer posted that character builder adding quarterstaff enhancement bonuses to powers was intentional and correct - before that I might have guessed that RAI was that it didn't work. Did they put all that text in about staff implements also working as quarterstaves because they were trying to make people understand (poorly) that it was both a weapon and implement and the implement-only versions worked a little different, or were they trying to explain (poorly) that they were a completely separate beast from the staff weapon group?
Either way, the text for wizards using the staff weapon group is the same text that swordmages use to be able to use any, say, heavy blade as their implement/weapon, so in order to claim it doesn't work by RAW, you're also effectively claiming that swordmages can't use longswords for their implement powers - only 'Heavy Sword Implements', of which none have been published.