I trust them because they are trust worthy. I've had issues with them, and periods of holding material back from them until an issue was resolved. The thing though is that they aren't a scam even if they make mistakes. And yes they will fix mistakes, not every customer service representative is top notch though and sometimes how you approach dictates the kind of response you get. They get a lot of off the wall people they have to deal with. Regardless though the top TPGs do want to get it right and aren't out to scam anyone. Dealers and sellers on the other hand, there's a lot of snakes in the grass there and the TPGs have helped the collector far more
I'm a bit lost here, you see a MS67 coin. NGC records show a value for a MS65 (nothing higher shown) of $2000. PCGS records show a value for a MS66 (nothing higher shown) of $12,500. I dont know if the seller actually knew what he had but his acceptance of $350, and your offer of the $350 indicates to me that you both tried to screw the other. He probably knew it was a proof and hoped you wouldn't know the same.