Filming a board meeting

Who filmed?
Are they HOA members?
Are they hired by others?
What does IL statue say?

Please help us with the homework you need to do prior to asking us?

We need a lot more information.

An HOA board meeting isn't a "public" meeting in the same way as a school board meeting, so I would think the board would be able to set rules on recording (audio or video) of meetings. You've run into one of the primary reasons it's not done - recording can "chill" discussions of a certain subject because, as George indicated, you don't know who's recording or what will be done with it (some people might be tempted to slice and dice the footage or audio recording to take things out of context.)

Answer George's questions and go on from there, perhaps talking to the association attorney. It may be possible for the board to set some ground rules, such as the recorder asking everyone there for permission to record before they do it and documenting that consent in writing. That said, it appears the underlying issue is a concern about transparency - people often want to record meetings because they don't know what the board is doing or why. Well written minutes posted on the community website may help resolve some of this, but remember, minutes aren't a note for note recap of who said what. Minutes are considered legal documents that should be an accurate reflection of the decisions that were made, who was there, etc. There's advice all over this website in other conversations and on the internet on how to do that.

You answered your own question. It's your problem. If your state's law and your association's governing documents allow it, then your only course of action is to deal with it. Sorry, I know some people are camera shy. Wear a mask.