Quick lesson: modern braking systems have a brake booster. This is a system that multiplies the force you apply to the brake pedal using vacuum generated by the engine. The vacuum comes from the air-intake manifold just past the throttle body, where at idle there's roughly a 22 inHg vacuum. Cars also have a vacuum reservoir so that the brake booster works even when the car isn't running.
So, maybe you already see the problem. The vacuum reservoir is a limited (non-infinite) size. When the gas pedal is all the way down, the throttle plate is wide open and there's virtually no vacuum in the intake manifold. The brake booster still works because of the reservoir. However if you pump the brakes a few times, for instance a tentative "why am I accelerating" tap on the brakes or if you are pumping the brakes in a (pointless) effort to keep them from locking up or overheating, you can quickly "drain" the reservoir.
I found on both my cars that the first 3 presses of the brake pedal had nearly full effect and would easily stop the car at full throttle. The fourth pump of the pedal was harder but it was still conceivable to stop the car. The fifth pump felt like there was a brick under the pedal and the car kept accelerating because I no longer had any assistance from the brake booster. I was quite literally trying to overcome the power of the engine with just some very inadequate hydraulic mechanical advantage.
Please do not try this at home.
and of course, Wikipedia:
In the spirit of fair play, I did due diligence of searching for opposing opinions that would support your view, but came up empty handed.