Can someone explain
How this is in principle any different from giving people a database of encrypted rows, and providing a way for them to get the key to unlock certain rows? This is probably a little simpler, and you can post the blockchain publicly, but they appear to be making claims about its security that they can't deliver on.
Sure, it sounds like this could prevent someone who gets hold of the blockchain from reading the data within, just like if they got hold of the encrypted DB. But once you've accessed the data and have it in plain text, if for instance it is a list of email addresses, you can do anything you like with them. There is nothing that can be done to the blockchain to revoke the access of someone who has abused their access, once they extract the plaintext it is no different in principle than mailing them a CD. If they can know you accessed those email addresses that's great (they'd only assume it with the CD) but that doesn't change anything.
Once again, blockchain is a solution looking for a problem. Though at least this time they're trying, it is better than the previous crap uses I've seen.