I am a little surprised that the brakes didn't work. Are brakes "fly-by-wire" now? Otherwise you should be able to slam the brakes even if the car is full throttle. I have tried this with several cars and the brakes we always stronger than the engine.
Brake-by-wire seems like a bad idea. I really want to have those physical lines in there as a final redundancy, like the physical control lines on a 737.
These kinds of stories are only going to get more common as we put more and more automation (and complexity!) into our vehicles. This would require way too many improbable events to happen at once on an old manual transmission car.
Clutch lines fail, shifter somehow gets stuck in gear, brake lines snap, ignition has an electrical fault that prevents the car from being turned off, cruise control somehow short circuits...all at once. Impossible without an elaborate sabotage.
Would government getting control over our cars be that much more unbelievable than of our phones?
Absolutely not. Cars have dual redundant hydraulic systems which are operated mechanically by the brake pedal. Other systems affect this (such as vacuum assist, ABS, AEB etc.) but the foot brakes should still work (poorly) even if the car is totally unpowered.