"Reversed wiring on a capacitor" would not cause a compressor to lock up. Reversed wires on a capacitor isn't even a thing, as they are not polarity sensitive. It could have been wired wrong, but I suspect they were just making something up to avoid taking responsibility.
Compressors usually lock up due to lack of oil. This can be caused by an overcharge and/or improper superheat adjustment allowing liquid refrigerant to return to the compressor to wash the oil out of it, or it could be caused by poor piping practices (long refrigerant runs with dips or "traps" in it, allowing the evaporator coil to freeze up and continuing to let it run that way for a while, short cycling due to it being way oversized for what you need, etc).
Compressors usually lock up due to lack of oil. This can be caused by an overcharge and/or improper superheat adjustment allowing liquid refrigerant to return to the compressor to wash the oil out of it, or it could be caused by poor piping practices (long refrigerant runs with dips or "traps" in it, allowing the evaporator coil to freeze up and continuing to let it run that way for a while, short cycling due to it being way oversized for what you need, etc).