To give some more clarity to this:
The app is built in such a way as to allow certain mobile manufacturers to have our app pre-loaded on their devices. For analytics purposes, we'd like to know how much traffic comes from these preloads. The way that we do this is by including a custom identifier string directly into the app, and passing that string into the analytics.
The problem is: when the app gets updated on those devices via Google Play (which is inevitably the first thing that happens when the device is powered on), the identifier string gets overwritten. Therefore, we've added an on-boot handler (which requires the new permission), so that the app gets a chance to save the custom identifier to the settings database, which will persist across updates of the app.
Note that we don't require this permission in the production or beta versions of the app on Google Play, and it wasn't intentional to require the permission in the f-droid variant (since f-droid doesn't use Google Play). Since Stephen's patch is already merged, this will be resolved in our next release.