If true, it really does sound like something from a cartoon.
And you sound like a journalist.
But hey, what the heck.
Every commercial transport aircraft has multiple services to critical systems, including brake systems.
From memory, there are indeed a pair of Brake System Computers on the A320, and there have been several reports of both failing together, leaving crews with no brakes. The way to deal with that scenario requires some quick action on another switch (NWS Disconnect switch) and some fancy foot work on the brake pedals. A competent crew can cope with it in theory.
The question about dispatch with a backup system u/s is more complex - there are regulated lists of allowable defects. This is called an MEL - Minimum Equipment List. Sometimes 'spare' systems are allowed to be used to keep an a/c flying, per the MEL. If EVERY system was required ALL the time - its doubtful if most a/c would ever fly.
Wish I'd been there, with a camera. At a safe distance of coure.
Ciao.