What exactly can an org do. We hire outside verifiers and then meet their standards.
What an organization can (and should) do is to behave in a way that earns people's trust over time. Microsoft actually had a window of opportunity to do this. They even made a very public campaign proclaiming how they weren't like the Microsoft of old and were more trustworthy than they used to be. And for a while, I even thought that perhaps a real culture change really did happen. But their behavior (especially around Windows and Office) is uncannily similar to that of other companies of questionable trustworthiness.