I for one can't wait until this app is decompiled, so we can judge it on facts rather than rumours. It'd be interesting to see what techniques they employ and how far reaching their invasion of privacy is.
It's also not possible on Android to access other apps' data. (even as a user which is frustrating). But it can ask for access to all common storage which usually contains images, downloads and some other stuff.
Tracking location isn't what this is saying - it's saying you're giving them access to EVERYTHING on your phone - all the apps, all the data.
Yeah, sharing location's not great, but you have to accept that if you're connecting to cell towers they pretty much know where you are all the time anyway.