I'm not sure that an anecdotal study of the behavior of four nonprofit boards is conclusive, but, for want of deeper and wider data, this study does offer some thoughts to consider about board and board member dynamics. Here's a link to the NPQ article and below is the summary of the study.
From this study of four organizations in a growth crisis, we learned about the changing nature of board/staff relationships that affect governance of nonprofit organizations. The dynamic moved from CEO preeminence and dominance to board-led control, and, subsequently, to collaboration within a paradoxical trust-distrust relationship. Three lessons are important here: First, no single mode of CEO or board predominance was sustainable—internal and external dynamics played together, which generated either long-term latency or sudden and overt change when the crisis occurred. Second, board behavior can be contradictory and can change over time. Third, the dynamics of trust and distrust appear to explain how relationships change from one phase to another in these crisis scenarios. These lessons provide some insight into how boards and managers might consider developing their relationships to better control the disruptive effects of a crisis.