Sorry I missed your question. No, i did not take my foot off, I was flooring it, and the car slowed down considerably, but when it was a few feet behind the other one, I pressed the brake even harder wanting the car to stop asap, but it accelerated slightly and switched lane at the same time very smoothly but rapidly, did not feel like unintended acceleration at all, that would have freaked me out even more, felt like how AP would sometimes accelerate before a lane change. But the lane change was swift, it did not slowly merge into the other lane.
No problem. Unfortunately I think we are all going to be at a loss of any reasonable opinion because your statements are implying multiple things that I think most people are going to at least assume cannot happen(as designed). Please don't get me wrong, I'm not going to sit here and say that what you are saying did not or could not have happened, it just seems very unlikely for the reasons below.
Brake override. I would be surprised if Tesla is not allowing brake override in all situations on purpose. While it is not a legal requirement to have a brake override system, I think people and NHTSA would have a major issue with your scenario as described.
In a possible rear end collision scenario I think the normal operation would be for the car to just apply AEB(automatic emergency braking). Now if you were on and stayed on AP then I could possibly see an avoidance maneuver BUT...
You pressed the brake pedal which would have automatically disengaged TACC and AP auto steer. You also kept the brake pedal pressed which would presumably preclude any acceleration event for two reasons. It would either have to apply acceleration while the brakes were still engaged OR it would have to override the user's brake input. Override the users brake input I think would be extremely frowned upon and most likely would open up Tesla for liability. Engaging acceleration while also allowing the users brake input is more believable, however; that means the car has to add a considerable amount of power to accelerate through the friction brakes which then open up a massive "uncontrolled" acceleration boost if the user suddenly lets off the brake.
There is a lot here that doesn't make sense. Could the car be programmed to do what you perceived happened, sure. Do I think it happened the way you said it happened, sadly no. It is a shame you don't have a dashcam video. You should enable dashcam save on honk. Also if you have a situation like that again just hit the dashcam button and it will save a clip on demand.