You are correct, I also seriously doubt that the system was charged to the correct pressure without the compressor engaging. I too, would look for a new mechanic. Unfortunately, I have done a lot of AC work, and have needed to minimally pressurize the system in order for the low pressure switch to allow the compressor to engage. The danger in not doing so and getting the compressor to engage by jumping the low pressure switch without refrigerant in the system is that quite often the refrigerant also contains compressor oil to lubricate the compressor (more often than not the compressor is pre- filled with the proper amount of oil - but you never know). As I explained I am not familiar with his car and therefore suggested several possibilities including the low pressure switch, a fuse, or if so equipped, the Klima relay.