For anyone still trying to understand (or doubting) the physics of this, consider the following:
As we all know, the braking system acts upon all four wheels, and in most vehicles, it has sufficient strength that it can rather easily lock the wheels (if we ignore ABS). Imagine the "opposite" case. That is, a 4WD vehicle with locked differentials (no open diffs or overwhelmable LSDs) and a powerful enough engine to break traction and spin all four wheels at once.
If you had two vehicles like this, with equivalent tires and differing weights, you'd likely get similar acceleration rates off the line. How much they weighed would be less of a factor than how well the tires could grip the pavement; drag racers know exactly how important it is to have tires that let you transfer as much torque to the pavement as possible. Remember, we're assuming the engine in each car is capable of spinning all four wheels with too much throttle, even if that means it's more powerful in the heavier car.
For a real-world example (minus the ability to perform four-wheel burnouts), consider the curb weights and similar 0-60mph performances of some of the fastest AWD cars available today -- the Bugatti Veyron SS (2.4s, ~4200lbs.), the Porsche 911 Turbo S (2.7s, ~3500lbs.), the Nissan GT-R (2.9s, ~3800lbs.) and the Gumpert Apollo Sport (2.9s, ~2400lbs.). Such incredibly fast, brief acceleration times do muddle comparisons a bit. However, even with curb weights spanning a difference of nearly 2000lbs., they're all in the same neighborhood, and probably couldn't do much better on the same tires (or any tire, given current tire technology).
Even compared to those cars, a locked-diff 4WD machine that can spin all four wheels if you boot the throttle a little too hard is insane. Yet that's a reverse analog of what we're looking at when we talk about the average car's braking system. That's why tires are the number one factor.
It's not a perfect analogy, but I hope it helps.