For a board member/trusee to knowingly bid for a collection item against his/her institutiuon is a blatant conflict of interest and a violation of legally mandated fidicuary responsibility. “Knowingly” may be the key word here. It’s possible to be bidding in an online auction, or by phone at a live auction, without having any idea of who the other bidders are or what (if any) organization/institution they may represent. Did the museum in question advise its board/trustees that it would be bidding on specific auction items? If not, it’s entirely possible that there was no “knowing” conflict of interest.
With an appropriate personal collecting policy in place, the board member /trustee would have been required to promptly offer the “won” item to the museum on an at-cost basis.