Programmers are not network engineers.
Thing is the DDOS would be on against the URL/logical (IP) address so even if the service could be moved dynamically the end result would still be denial of service, the bad packets would still reach their destination. So cloud computing could work for diaster recovery (power failure, nuclear war, whatever), but it's not a replacement for good security from the cloud and hosted service provider.
Also the thing about the storage being on the same interface sounds like nonsense. I am making a couple of assumptions here, that they access the service via the public internet rather than via private means (ie VPN/MPLS etc), and that they lost access to everything. In which case the DDOS would have been against the address used to provide access to the hosted service, not the storage, and hence deny access to the entire service.