Fisher and Snead both described how they put players in groups.
This was so when their turn came up, there usually wasn't some theoretical single "best player"on the draft board. Rather there was a group of players to choose from, usually representing more than one position. Then they would inject "need" into the equation. Of course, if there was one clear best player even not at a position of need, but that player was seen as transcendent, they might take him instead. Donald was a good example.
So to say that the board automatically determined the pick is too simplistic. There were subjective issues involved.
There is no way in heck that a couple of years ago that they chose a slew of Olinemen who just coincidentally happened to be the best player on their board at the moment they were drafting, the same year that they wanted and needed a slew of Olinemen.
The rest of your answer seems quite plausible.