I don't know that I've ever seen anything saying that this position wouldn't be an elected one. Of course, maybe I haven't seen a lot of information, but without something specific there's no real reason to assume this to be true. To avoid further speculation on it, maybe a board member would be so kind as to tell whether the position of treasurer is generally an elected or an appointed one.
The board consists of a mixture of appointed and elected members, so there is clearly a choice. Given that choice, why would you ever use an election to select somebody that requires a specific skillset? It would be foolish to the extreme. Democracy is simply not a good way to find a treasurer.