Q: While pressing on brake pedal, car accelerated

Intermittently the brakes in my car quit working. I have been to the dealership several times, but it wouldn’t happen for them while they had the car. One day while driving 30 mph, I depressed the brake pedal but the car just kept moving and would not stop. Because of this I rear-ended another car. Everyone was alright fortunately and the police filed their report. I decided to wait on the diagnostic test from the dealer before having the car repaired. They told me that it was not brake failure that caused the accident, but unintended acceleration on my part. That is not true since I was pressing on the brake pedal. Can you tell me what caused the brakes to fail, since I know I didn’t accelerate?