It is a way to show confidence that it won't happen again. The same's true for a new CEO announcing this. Uber is on a "flattery strike" (for lack of a better word; sry I am not native English) on the general public. They're trying to win our hearts. I see their employees also regularly commenting here, excusing themselves and explaining the situation.
If you're being blackmailed you always lose since a problem with blackmailing is that it doesn't stop as the evidence isn't destroyed. Its like a fork in chess, two evils. However, generally speaking (excluding political motivations such as Clinton leaks), the blackmailer wins nothing by releasing the information. So you can let them win by giving in to paying. I guess this is game theory.
True, if you pay the evidence might seemingly get destroyed (or a seemingly "original copy" of it), but you can't be sure (there might be a "copy of that copy"). Another example of this is revenge porn or CP for that matter. Yet another example of copyright infringement/piracy.
Once its out in the open, it will keep getting distributed. The cat's out of the bag. Its a problem of the digital age. As a society we haven't quite coped with this issue yet and privacy invading seemingly free services are clouding our judgements.
