I don't know who "someone" is, but if that person can do accurate diagnosis without looking at the machine, maybe he or she should go to work at Apple. If he or she already works at Apple, then the statement should be "might" instead of "would".
The headphone jack is a separate device connected to the logic board by a cable. So depending on what has failed, you may not have to replace the main logic board. You might have to replace the whole case.
Are you positive you've exhausted all possible software issues? Checked settings in the Sound preferences pane? Reset PRAM? Physically unplugged the machine from power? Pushed the headphone plug fully into the jack?
From personal experience, it's best not to rush repairs at Apple Stores. In my quest to not have machines away too long, some have come back with rushed work--speakers not connected, screws not tightened, and so on.