See also this thread:
https://forums.developer.apple.com/message/417547#417547
It seems there's an entitlement needed, and presume the account needs to be enabled to be able to grant the entitlement.
This would seem to preclude even Enterprise apps unless Apple is willing to approve the particular enterprise.
You can see how this could be abused to go counter to Apple's intention. For example, logging of geographic location. Logging of e.g. employee ID.
Not sure at this point what my opinion is.
On one hand, I can certainly see the usefulness of, say, a food processing company, a delivery company, warehousing, call center, school, etc.etc. wanting to track centrally their employees, students, etc. But this goes counter to Apple's intention. Even with permission of employees or explicit language in company policies, it seems Apple would be unlikely to approve of this.
So, while Apple normally doesn't exercise control over Enterprise apps, perhaps in this case they are going to. At least until they do some more deep thinking. You can see that there might be controversy and lack of confidence in anononymity if Apple were to permit it.
I myself primarly develop Enterprise apps. In fact, my interest in this is to write a compatability layer for one of the cross-OS development platforms. e.g. similar to Cordova/PhoneGap, Xamarin, React Native, etc. (but that is for example, it is none of those, and presume those are already in the works!) I intend to open-source and release under MIT license, and have a sponsor for the work. So, then, it would facilitate writing apps (for/by public health agencies) on a cross-OS platform, without having to reinvent the wheel by writing the necessary native code to connect the platform to the framework(s). (As I intend to implement both iOS and Android).
And, so I've given some thought to how Enterprises might want to go beyond the constraints of public apps. But would not be surprised, and would accept that Apple is not willing to allow Enterprise apps to be less anonymous, and so probably little point then in any Enterprise apps.
I'm happy myself, then, just to provide the compatability layer that would enable others (or perhaps myself as well) to create apps on behalf of public health organizations.
But search as I might, I cannot even figure out who to contact to find out what is needed to gain approval.
Presumably, Apple has reached out to some public health agencies. For those they haven't - who would they contact at Apple?
It seems all of the technical information has been published, but none of the administrative?
Clues, anyone?