The question of who owns the data is partly determined by the kind of cloud infrastructure that is in place for your business.
The advantages that cloud based hosting brings needs to reiteration. Cloud hosting is infinitely scalable, needs radically lower CapEx and with distributed hosting, it is much more fail-proof than data hosted on your premise. But the recent legal spar between Apple and the US government has brought the limelight once again back on the debate about ownership of data. In the case of Apple, the fight is over decrypting the iPhone used by a criminal in order for the government to hack in. But the case may as well be between law enforcement and a web host over data stored by your customers on your startup service.