In fact this is over simplification. The only key that will be uploaded is partial of the daily tracing key (called Diagnosis Key in the specification).
Most importantly, there's no location or timestamp involved or needed. Once this Diagnosis Key is uploaded, every client (anyone who wants to know if they are potentially infected) will periodically download the batch and see if your phone has seen any of the Rolling Proximity Identifiers, and when.
You may have a point when it comes to the infected, but even then, giving Apple or Google this type of information is putting far too much trust and power into too few hands.
It's computational impossible to reverse from Rolling Proximity Key to Daily Tracing Key to Tracing Key.
In terms of privacy, small-scale adversaries can deanonymize infected users that have uploaded their [keys by keeping logs] of and limiting who they have come in close contact with.
On a large-scale, adversaries in control of large Bluetooth receiver networks (such as cities performing traffic analysis) can now track the movements of individual infected users over the course of a day. One could argue that this is already being done to track anyone with bluetooth enabled.
In addition, the process of uploading to the backend server could alert adversaries monitoring your network that you (the device using your IP address, uploading to the server IP address) have tested positive for the virus.
I recommend that you look at other contact tracing protocols that circumvent some of these issues by decrease or eliminating the linkability of identifiers, allowing users to censor records uploaded, and encourge the use of network-anonymization.
*Edit Spelling - Source: https://covid19-static.cdn-apple.com/applications/covid19/cu...