Title 18 of the Pennsylvania Consolidated Statutes, Part II, Article F, Chapter 57, §5704, lists exceptions to the prohibition of the interception and disclosure of communications (exceptions to recording without the consent of all parties), and following §5704 are sections explaining the order which authorizes an interception, and for what offenses the order can be used (§5708), how to apply for an order (§5709), and how to record and monitor the communications (§5714).
This means that in Pennsylvania, under some circumstances, there can be recordings made even when there has not been consent to record given by all parties.
Because ccchwine did not provide us with any details about the private meeting or who exactly would be recording it or under what conditions it would be recorded (or, in fact, if the private meeting to be recorded is even in Pennsylvania), it is impossible to say if the meeting could be legally recorded or not. It may fall under one of the exceptions allowed (or fall under another state's laws).