I specified the United Way to avoid confusion on that point. While the word nepotism originated from the Italian word for “nephew” referring to popes appointing their relatives, in modern English usage it more broadly includes friends as well. See for example the OED: “the practice among those with power or influence of favouring relatives, friends, or associates, especially by giving them jobs”.

If it helps, pretend that I wrote “cronyism” instead. My point was simply that it having a friendly voice at the board level is a large potential advantage which was only available to one of the vendors. While we cannot prove anything which wasn’t written down, it seems implausible to say it couldn’t have affected things – especially in an era where personal relationships carried more weight and there was less scrutiny of these sorts of things.