This is a luxury many researchers that work outside of these big tech companies don't have, which creates a scientific power imbalance. Mozilla Rally is meant to give these capabilities to everyone, and the platform is meant to ensure that you always know what you sign up for and what data is being used.
If I understand the Princeton example correctly: They want to figure out how people consume and spread misinformation. Social networks like Facebook have all that data but won't share it. Now you can opt-in to a Rally study where independent researchers can examine the data.