I'm not sure denying an app permission to use your data is the same as explicitly choosing to provide that app with randomized data.
If you want to ensure that the system is only doing what the user explicitly chose to do, you need to provide prompts that let the user explicitly choose to provide randomized data.
And at that point, we're probably better off just returning nothing.
It's not really hard.. one choice with a multitude of options:
Choose Level of Location Access:
1. Full access (exact location)
2. Nearest [major intersection, city, state]
3. Fixed location [home, work, present location, choose from map]
4. Random walk [choose area from map]
5. Ask me every time
6. Deny
Go ahead and default/emphasize the most-desired and least-confusing options so that fewer mistakes are made. But treating users like children and restricting their options in the name of 'usability' is downright wrong. Your average person seems quite dumb due to disinterest, but give them options and abilities they didn't know they could have, and watch as their interest perks up.
I'm not sure denying an app permission to use your data is the same as explicitly choosing to provide that app with randomized data.
If you want to ensure that the system is only doing what the user explicitly chose to do, you need to provide prompts that let the user explicitly choose to provide randomized data.
And at that point, we're probably better off just returning nothing.