The Gozer Principal: in Information Security you get to design the weapon that will be used against you [1]. Don't build a tool you are unwilling to hand to your greatest enemy.
For example what happens when foreign governments steal the domestic bulk surveillance data? I bet the NSA accidentally hoovers up all sorts of top secret information that is just accidentally sent over the wire or non-classified data that could do great damage to US interests. Or what happens when a foreign government gains access to the tools used to perform this bulk collection? They could inject fake traffic or hide traffic for strategic deception campaigns.
Collect it all is a strategically empty slogan, it represents a serious risk to US national security, but on the other hand it is a wonderful Rice Bowl [2] for the NSA.
>What can an organization do to protect such sensitive information, or at least reduce their exposure and the amount of data that is able to be leaked before detection?
* Keep it offline/airgapped.
* Store the most dangerous data on paper with hashes replicated online to insure integrity.
* Delete information you don't need anymore.
* Do not have a centralized repository of data to reduce risk of catastrophic exposure.
There are always trade offs between usability, functionality and security.
[1]: https://twitter.com/ethan_heilman/status/510993743156375552
[2]: https://en.wikipedia.org/wiki/Iron_rice_bowl#Other_uses