Cynical me says that they don't want it on the website to give you a reason to install the app, which grants AA snooping powers it would otherwise not have.

On Android, these include:

• read phone state and identity - Allows the app to access the phone features of the device. This permission allows the app to determine the phone number and device IDs, whether a call is active, and the remote number connected by a call.
• retrieve running applications - Allows the app to get information about currently and recently running tasks. This may allow the app to discover information about which applications are used on the device.

Frankly, I don't understand why these permissions are needed for us to use the app. In addition, AA's app also request permission to catalog network connections such as which networks exist and are connected, both mobile and Wi-Fi, plus some potentially useful ones (but are they used by the app?) such as your precise location.

Creepy.