Anonymous Feedback Without Anonymity

I know a company which takes regular anonymous feedback. They have enough checks to make sure that, the feedback is really anonymous. The feedback is conducted by a third party, and it contains many objective questions. The third party aggregates all the responses at the senior manager level for each question and gives it back to that company. All the senior managers and above would know the aggregated feedback, and they are obliged to publish the aggregated feedback to his/her team.

In that company, some time back, under one senior manager, for the question, Intent to stay in the company, nobody said, they would stay in the company.

Where is the anonymity in that? If there was atleast one person who intended to stay in the company, the anonymity would have been there for everyone. But, now, it is clear that the entire team under that senior manager wants to leave the company soon, it would be too embarrassing for everyone in that team.

By the way, soon after publishing the results, the senior manager left that company.