This is turning into one of thoes Internet arguments, but I actually agree with both of you. You can park overnight using the daily parking fee, and I have done it many times. BART allows this to encourage people to not drink and drive.

You also must get a permit for the weekends if you are doing airport parking, and that cost is $0 per day weekend and holidays.

So you are both right, its a conflunce of overlapping rules. Carry on.