I don't work for PGMusic, but often these 'Permissions' sound worse than they are.
Android warns about everything, which is good I guess.

My thoughts (guesses on scenarios) off the top of my head;

Read phone state and Identity - The app needs to know if the phone is in a 'sleep' mode, connected to a network, etc. so it can perform correctly.
It also needs to communicate with the BB server application on your machine so using the device ID (Identity) is necessary over the network.

Managing the account list and using authentication - It could be possible that there are more than one available BB server to select from, which would be another 'account'. Also, if the Android has multiple user accounts and the app is installed under a given user account, the app may need to authenticate with the assigned account.

Make your sound your own!
.. I do not work here, but the benefits are still awesome