Brake Grinding Noise problems of the 2008 Infiniti QX56

The brakes on my 2008 Infiniti Qx56 failed at an intersection today, causing me to go through a stop sign at an intersection. The brake pedal went to the floor and a sporadic grinding noise was heard and felt in the brake pedal. The brake indicator light was illuminated in the instrument cluster. The vehicle coasted to a stop. I pumped the brakes, but had no brake pressure. I put the vehicle in park, then turned it off. When I restarted the vehicle, the brake indicator light was no longer illuminated, and the brakes appeared to be working again. I immediately took the vehicle to my Infiniti dealer since this is my primary form of transportation and I have 3 young children. The dealer informed me that the fault code indicated my vehicle had a faulty brake booster, which would need to be replaced for approx. $1000 (parts and labor). They informed me that although they had seen multiple Qx56's with this problem come into their dealership, Nissan did not have a recall in place. I find this to be unacceptable. I am lucky none of my 3 children were in the car with me at the time, and that no accident resulted from my brake failure.