They are built with the appropriate industry card (or the wild one). The rules state that these cards, when used, allows me to build WITHIN my network.
So, does this mean that only the player that has a link tile that connects to an unnamed farm brewery will be able to build it? Or is this an exception?
That is correct, it is not an exception.
However when you have no links or industries on the board (ie first turn) you can use a wildcard to place a brewery there