Meeting summarization has an enormous business potential, but in addition to being a hard problem, roll-out is challenged by privacy concerns. We explore the problem of meeting summarization under differential privacy constraints and find, to our surprise, that while differential privacy leads to slightly lower performance on in-sample data, differential privacy improves performance when evaluated on unseen meeting types. Since meeting summarization systems will encounter a great variety of meeting types in practical employment scenarios, this observation makes safe meeting summarization seem much more feasible. We perform extensive error analysis and identify potential risks in meeting summarization under differential privacy, including a faithfulness analysis.