Never had an experience like this with autopilot. Is it possible the car cut in front of you and then started braking, making it seem as though your car was accelerating?
You say that the car cut in front of you and your car started accelerating so quickly that you didn't have time to react. Unless you weren't paying attention, for this to happen the other car must have cut almost directly in front of you. In that case, there's a good chance the other driver is at fault (at least partially) for making an unsafe lane change. How closely did the car cut in front of you? Do you have dashcam footage? (Strongly recommend a dashcam).
Otherwise, ask Tesla for the logs. It will reveal one of three things:
1. The car did indeed accelerate, in which Tesla has some 'splainin' to do, or
2. The car did not, and it was just your perception that was fooled--if that's so, it's not a personal attack on you--anybody's mind can be fooled, or
3. The logs will prove that you're a complete liar.
So it's one of these 3
. I don't know which
. Nevertheless, in hindsight it probably would have been a good idea to cover the brake the minute that car started to cut over. And make sure your following distance is set to something in the 5+ range. I understand that people like to have it set lower because other cars cut in front, but lower following distances both reduce autosteer's ability to stably maintain a lane (because there's significantly less visible lane marking for the camera to track), and also significantly increase the risk of an accident (obviously).
And again, if this really happened so quickly that you didn't have time to react, that car must have cut DIRECTLY in front of you, in which case there's a good chance the other driver is at least partially at fault. But whenever the car accelerates on TACC, it's always gentle, which means you should have plenty of time to react unless the car cut in front and stepped on his brakes.
Is there something about this story you're not telling us or a detail you're leaving out? I've driven tons of miles on autopilot in busy traffic, and for a car to turn into your lane, the Model S to accelerate, and for you to rear-end it without enough time to apply the brakes, it would have had to change lanes so closely to you that its rear bumper would be less than 3 or 4 feet from your nose.