drupe requires the permission to "read" the notifications you receive in order to comprise the unique Recents view.
You have absolutely nothing to worry about: We're very strict when it comes to use privacy. We do not - never have, never will - abuse your permissions.We do not collect, store, read or make any other use of our users' personal info.
Other apps don't require this kind of permission because none of them has the Recents view that we offer, which combines all the interactions with your contacts, and not just calls or texts - for instance, if you received a WhatsApp message, drupe can display an entry for that in the Recents view, based on the notification permission. That's all there is to it, really.