... so, as you imply, it seems that in the contexts we are talking about, "Board" probably does not actually refer to the 'organisation' itself but, rather, to the group of people running it?
yes, it means the "Board of Directors"
Collective noun
At the time I am thinking of, they would have been local councillors, civic dignitaries, noted engineers and other experts, acedemics, union leaders, businessmen etc.
The "Board" was set up first, and it was their job to put the organisation into place.