I have had the beeps but no actual braking....good to know it works!
Which setting are you all using?...it can be near, normal or far, but not sure those are the words.
Mine is set to default whatever that is (probably normal). I was a bit enthusiastic parking nose to a corrugated steel shed and was slowing down when the brakes came on with a vengeance.
Remember the Jazz has two different collision avoidance systems.
1. The City Brake Active system (CTBA) is the one that applies the brakes automatically if it feels like it. It works at low speeds between about 3 & 20 mph. It uses a laser sensor. There is no sensitivity adjustment. (Handbook p.450)
2. The Forward Collision Warning system does not apply the brakes automatically, it just beeps & flashes a warning. It operates above 9 mph; this is the system that has the near/normal/far adjustment. It uses a camera sensor. (Handbook p.428)
The dashboard warning display seems to be the same in both cases so it may not be obvious which system has functioned in any particular circumstances, the best guide is probably the car speed at the time. Personally I don't think I've ever had the CTBA activate, but the FCW is prone to false alarms, it can activate if the curve of the road makes the car think I'm about to hit an oncoming car (LH bend) or one parked on the nearside (RH bend), or if I'm moving up to an overtake position.