BAR is attempting to prove that the car never ran under 600kg. The car, when weighed at the end of the race, weighed OVER 600kg, meaning at no time during the last stint of the race did the car run under 600kg. Only at the request of the FIA was the BAR 007 drained of it's fluids and reweighed, and found to be about 40kgs under weight.
BAR is adament about knowing for certain that their car never ran under 600kgs, and always had enough fuel in it to meet the 600kg requirement.
The FIA also knows exactly how much fuel went into the cars, the sensors on the fueling rigs are quite exact. This means the FIA can tell how much fuel BAR put into the car at every pitstop, and would be able to calculate if at any time prior to the stop that the car could have run under 600kgs.
What is really in question here is wether or not fuel can be used as ballast. The rules specifically state that fuel cannot be used as ballast, but at the same time the rules say that ballast must be something that cannot be removed without the use of "tools". The question is wether or not fuel is removeable with tools (IE: The fueling rig).
It is not confirmed if BAR was running a "2nd tank", but if they were it appears that it would have been a sealed tank that actually didn't even connect to the engine, and thus was there for the express purpose of holding ballast fuel that could not be easily removed without tools.
As for banning, it's more likely that BAR will be stripped of their points but allowed to continue the rest of the season, since banning BAR would leave Formula 1 under the 20 car requirement, forcing teams to run a 3rd driver.
Oh, and getting your news on a Honda ban from a Toyota fanboy site isn't exactly the best source...