I don't think that's accurate, at least on the luxury cars where I've seen it implemented. Take a look at this list [1]. In many cases you could overpower the automatic braking by applying more throttle, but the brakes will definitely apply automatically to some degree if they think you're going to hit something.
Hmmmm yeah, I knew you could definitely do that in Nissans, and wiki offers an explanation:
"it alerts the driver using both a screen display and sound, then generates a force that pushes the accelerator pedal up" - so I guess it's like you said, you can just press the throttle harder and ignore the warning if you really know what you are doing.
[1] https://en.wikipedia.org/wiki/Collision_avoidance_system