I have an experience of this that does show that the buck very much lies with the referee. I was on the line for a contrib game when a player had a go at me, I waited for the ball to go out then called the referee over. The referee came over and asked me what had happened, I told him, and he asked whether I wanted yellow or red. I said yellow, it had been an easy game for the referee and I didn't really want to be the reason to make it difficult for him. So he yellow carded him.
After the game it was clear in the boardroom that the other team were far from happy, and I said to the referee there that we might be in trouble. He thought nothing would come of it, but sure enough a few weeks later he phoned me to say he'd had a letter from the FA charging him with failing to proficiently apply the laws of the game. Whilst the report from the club amounted to a pack of lies (it said I immediately signalled the referee who stopped play straight away, that simply did not happen) he was advised by colleagues not to appeal it as the person making the complaint was a high ranking league official.
I wasn't charged, he accepted the charge, then a week or so later I arrived home to a letter from the FA saying that "they found me culpable of causing a referee to be suspended", and that they trust I will act more diligently in future occasions. The referee, a hugely experienced Football League assistant, was suspended from all football for three weeks. So goes to show that the buck very much does stay with the referee even when it is the assistant who has made the mistake.