The only reason I hit my head with a brick here is that it is so common the NEC allows an exception for it. These units are designed up to the legal nema maximum to run on this legal circuit, a 20A. In a perfect world with every part hand polished and fine tuned it might be fine, or often these are used with cords or long circuits, etc where the user never knows. This unit in question has done this since new and seems to work in every other way, it has one issue, on starts, hence the allowance for breaker changes.
With this circuit and a 30 it will not overheat a 12 wire, the motor has its own thermal to protect it under run and is sized where it will not draw enough for this to occur, similar to hooking a 100 watt lamp on a 16 fixture wire to a 20A circuit. (some cases may allow up to 40A breaker on a 12) but no one thinks this is a great idea and isn't needed, no point in going more than necessary. In this type of circuit the breaker does not really protect the wire as it would in a general use circuit with several outlets where plugging in multiple appliances could overload and overheat the wire, its there to protect against short circuits.
Wouldn't surprise me this comp has a 14 cord, no matter what it wont overheat the 12 wire, all a larger wire will do is deliver a bit more current again during start adding back to the problem. You might reman this comp, tune every little part, change cap, clean check valve, etc, next week, some little glitch throws it out again. If a guy puts in a 30 and has same problem then,,,, there is reason to look more careful.