They were on the 11th green during the rain-delayed second round when their walking scorer told them play had been suspended because of darkness and they were allowed to finish the hole if they wanted.
Moore said he asked the scorer why the horn did not sound, and that the scorer said there would be none.
After pleading their case to PGA Tour tournament director Slugger White and two other rules official, they were reinstated.
'We weighed all the evidence,' White said. 'They got bad information, and they asked what they felt were the right questions. Basically, they're the luckiest two guys on the planet right now.'
Moore was 3-under par for the tournament, five shots behind clubhouse leader Carl Pettersson, in his third tournament back from a hand injury. Rose was 2 over and on his way to making the cut.
'We're still playing,' Rose said after emerging from the rules trailer. 'It was a tough decision, but I think it was the right call.'
Moore called it the 'perfect storm of events' that led to their leaving the course Friday evening.
He said their walking scorer -- who is not a rules official, rather a volunteer for the tournament -- had been giving them what turned out to be bad information all along. The scorer had a radio headset and told them on the eighth hole that play was about to be suspended when the last group had teed off.
When told on the 11th green that play was suspended, Moore said he asked, 'No horn?'
'He said they were not going to be blowing the horn,' Moore said.
Tour officials typically blow an air horn to denote that play has been suspended. In bad weather, players must leave the course immediately. In the case of darkness, such as Friday's round because of a six-hour rain delay earlier, players can choose to finish the hole, but they cannot start the next hole or they are disqualified.
They were disqualified for walking off the course without notifying a rules official. The horn sounded about five minutes later, but Moore didn't hear it because they were in a van headed back to the clubhouse.
Instead of going to his car and leaving Muirfield Village, Moore retrieved his shoes from the trunk of his car and headed to the practice range.
'I was hoping they would understand, and I was ready to live with it,' he said. 'It was a tough decision. Rules are rules. Everything came together to make a big mess. I had a hard time falling asleep last night. Fortunately, we didn't pay the price.'
Rules in golf can be harsh, and most of the time there is no recourse. In the most recent example, Mark Roe was two shots out of the lead after a 67 in the third round at the 2003 British Open. He was disqualified because he and Jesper Parnevik forgot to switch scorecards at the start of the round, so Roe's scores were on Parnevik's card.
In other cases, players have been disqualified for accepting a ride in a cart from anyone but a rules official when they have to return to the tee after a drive could not be found.
An argument could have been made that Moore and Rose knew better than to listen to anyone but a rules official. Both said, however, they were worried about teeing off on the 12th hole because that would lead to disqualification if indeed play had been suspended.
'This isn't the first time something like this has happened,' White said. 'We just felt it was the right decision.'