Might want to check your facts...
The whole part about the app not being able to work in the background is completely wrong. Normally, background Bluetooth scanning isn't allowed, which is likely why it wasn't working on the video mentioned, but that's not the case for the NHS app. Apple at least (and I'm assuming Google will follow suit) are allowing this one app to run scans in the background without the need for the app to be open on the user's screen.
Also, saying that it's able to track your location is objectively wrong. It asks for the first part of your postcode, which is a pretty massive area, and nothing else. It doesn't request location access, and judging it based on the fact that they could request that in the future means absolutely nothing right now.