While I don't usually like to say 'Character Builder allows it' as a basis for a ruling because of possible bugs, I will say this:
You can have a superior implement enchanted as a weapon. 'Vicious Quickbeam Staff +1' is something specifically programmed into that system. Someone had to take time to make that occur.
That said...
Alright. Here we go again.
First:
The 'staff implement' referred to in the PHB equipment section refers to two different things; the non-magical staff implement on page 221:
Arcane Implement: Wizards use orbs, staffs, or wands as focus items for their spells, while warlocks use rods or wands. Using a nonmagical implement confers no benefit. You can purchase a magic implement to gain an enhancement bonus to attack rolls and damage rolls with your arcane powers. A staff implement can also function as a quarterstaff.
This is a -very- specific item. This is not all implements that could be called 'staff.' This is a very -specific- item, listed on the adventurer's equipment list for five gold pieces. This text comes from the description of -that exact item-. It is not correct to assume that anything described as a staff is this item except for that 5 gold stick.
The other reference is:
A staff is a shaft of wood as tall or slightly taller than you are, sometimes crowned with a decorative crystal or some other arcane fetish. Fashioned either as a quarterstaff or a walking staff, it is also imbued with arcane enchantments so that you can channel your spells through it. Unlike other implements, a staff also functions as a melee weapon (treat it as a quarterstaff ). When used in melee, a staff applies its enhancement bonus and critical damage dice just as a weapon does.
This refers to the sorts of magic items called 'Staffs' that have enhancements such as Thunderwave, Ruin, etc. This heading covers all those items.
Now notice that neither heading has any text whatsoever mentioning that quarterstaffs cannot be used thusly. All you have here is all text stating that specific 'staff implements' can be treated as quarterstaffs for the purpose of melee weapon use.
Thusly, if you have the premise 'I am using a magic staff or the 5 gold stick' and the premise 'My item is a quarterstaff', then the following:
A -> B
is true.
To suggest, however, without evidence that 'My item is a quarterstaff' implies 'it is not a staff implement' does not logically follow.
A -> B =/> B -> ~A
So one needs evidence other than the above to suggest such a premise.
By the same token, A -> B does not imply B -> A either.
Thusly we need other evidence to indicate B -> A... and that evidence exists. And not just in Character builder.
First:
Quarterstaff +2 1d8 — 5 gp 4 lb. Staff —
That 'Staff' is from its weapon group, indicating that Quarterstaff is, in fact, a staff.
Continuing on, 4th edition has a design around 'specific beats general'. If you have a contradicting specific rule, you do not follow the general; by converse, if you do NOT have a contradicting specific rule, you DO follow the general.
Ignoring wizards for a moment, let's look at the swordmage's implement list:
Implements: light blades, heavy blades
This indicates that yes, weapon groups can be used to describe implements one can use. One can list weapons in the implement area and it'll totally count.
As well:
Implements: daggers, staffs
from the Sorcerer shows us again, we can have a weapon in the implement area. And there is that staff entry... so... as it's already proven implement areas can include weapons, and it is also shown there is no evidence to indicate the staff weapon group is exempted from being in the implement entry, the only cogent and rational conclusion is that the staff weapon group CAN be mentioned in implement entries, and be refered to.
On top of that....
A quarterstaff costs 5 gold and is a staff. The arcane implement staff is 5 gold and counts as a quarterstaff. They are interchangeable by any reasonable logic, and there is no evidence to indicate otherwise.... in fact, the only evidence that DOES exist on the matter indicates that they are meant to be completely interchangeable.
The only argument against it is 'I don't feel it should be that way.' Which is a legitimate reason to exclude it in a game you are running, but as an argument strictly based on 'believe' and 'emotion' has no real place in a logical debate.
But yeah. For something that is so 'obviously not the same thing' someone took a lot of time to make sure that all the magical superior implements could be either enchanted with staff enhancements or with weapon enhancements.