You’re possibly right in your assumption that the Broker was just chasing a higher commission because $1M is the norm., although it will all be for naught as you’re again right in concluding that any illegal actions by Committee Members collectively or individually aren’t covered at all, and nor is any penalty that a Court may subsequently issue to any of them in circumstances where the legal defense that IS afforded under the Liability Policy is unsuccessful.
Furthermore, the term “illegal” is pretty broad, and includes things like Committee Members behaving dishonestly, maliciously, fraudulently, libelously, and by doing things as part of their role that improperly benefit them, collectively or individually.
So to conclude, if your Committee really does comprise “pretty dodgy people”, then NO amount of Office Bearers’ Liability Cover will be of benefit.