Pinky,
Yep understand your cynicism. The app has been running long enough now for someone to have discovered that it was "calling home" and that hasn't happened. Irrespective of government assurances this is good evidence to show privacy is being maintained. One of the reasons the app was slow to market was the fact that privacy was paramount and the app had to be effective while still maintaining the users privacy. It does that.
What's your problem with the Ministry of Health QR codes? They are a unique identifier of that businesses, sport clubs, or organisations location displayed as a QR code to enable anyone to record an electronic diary entry on their device of where they have been. It basically saves you having to manually record where you have been if contact tracing is required. Once you have the app on your device the system can work without any cellular connectivity.
I don't think much of our current government and think their handling of the pandemic has been barely adequate, our success has been due to a good luck and other factors. However I do trust what they say when they tell us the location details are not shared. Perhaps our government is more trust worthy than yours? Another point regarding privacy of location data is this app is the cornerstone to their contact tracing programme. There is no way they would want to compromise its use with the discovery they had been lying to the public about privacy.
You seem surprised businesses would be compelled to display the QR codes? For such a system to be effective there needs to be some level of compliance. Perhaps that's another difference. On this side of the Tasman we see that there is a need for this sort of thing in order to keep on top of Covid.
P.S. Use of the app is voluntary but everyone is asked to keep some sort of record of their movements.