The difference with online backups is that it's dedicated to music. No one wants to share their online backup account, but they might share or even sell their Anywhere.fm account. The legit use for the service is probably legally safe, but things can get gray quickly.

They should definitely requite all new uploads and store entirely separate copies of everyone's music. Doing optimization based on a file's checksum, like you'd do for a straight backup service, would be harder to explain to a judge.

They should very quickly implement a mechanism for locking accounts that get too many logins from different IP ranges in a short period of time. It shouldn't be too difficult to make it annoying for naughty users without impacting legit users. Staying on top of abuse and not letting their site get overrun like Veoh is key.