Augur is using Airbitz as the private key security part of its platform. Airbitz will encrypt, backup, and secure your private keys. It doesn't matter whether it's Ethereum, Bitcoin, Bitshares, or just data. The Airbitz mobile app is a bitcoin wallet (for now) but it also lets you "login" to Augur with your Airbitz acct.
Keep an eye out in the future for an even tighter integration between Airbitz and the currency (ETH) and tokens that Augur uses.
RE: Why is Augur's wallet, AirBitz, asking me to use Bitcoin instead of Ether? Augur is Ethereum based!