I doubt it is the PCM, though it could be, as the voltage is regulated by the PCM. It could also be the fusible link. There is a way to test, if you have a voltmeter. With the engine running, check the voltage at the alternator terminal. It should be at least 14 volts or more. Also check it at the battery. It should be the same. If lower at the battery, replace the fusible link.
If it's the same at the battery and both are above 14 volts, the charging circuit is probably fine and the problem may be a short in the car. I can send troubleshooting steps for a short if someone is good with electric circuits.
If the voltage is lower than 14 at the alternator terminal, then either the alternator is bad or the PCM is bad, and your mechanic may be right.