I doubt that any board has daily input into what Management are doing.
ie paid staff are paid to carry out the work that a Board gives an overall aim, direction.
So depending on how often a Board meets they might find that in between 2 meetings a whole shit show like this has taken place.
However in delegating paid to staff to carry out the daily functioning of the organisation, it is also likely that individual board members will have specific responsibility for example finances, personnel etc., and that the relevant paid member of staff would contact that board member to alert them to a potential issue that might have repercussions on the reputation of the organisation - or is on a legal border line.
So the board could be held responsible for employing people who are either incompetent or using their position to impose their personal views or whatever.
But in any case, given the publicity this Board must be aware that there is an issue and may well have asked for an up date and not wait to a regular report for the next Board meeting.
Although of course if in the past the Board has agreed a policy that specifically instructs employees to further a TWAW agenda then obviously they are directly responsible.
Although you would think after the ERCC court case, they wouldn't do this. As far as I know in that case there was no ruling that said ERCC (and therefore other groups) had to accept that biological females are women and TW aren't. What they were told is they cant impose this on users and employees, and cant bully them to believe this.
However as we have seen despite Roz Adams winning her employment case about having the right to be honest to users, not many if any organisations in Scotland have made any changes to how they work or their position on TW.