It is very easy to get charged with a crime, though very tough to get convicted of one. At trial, the state has to prove every element of a charged crime beyond a reasonable doubt or the defendant must be acquitted. But to make an arrest and to get charges filed with the court, all the state needs is something called probable cause.
Probable cause requires very little evidence. It is simply a reasonable belief that a particular person or persons may be been engaged in criminal activity. The words of a credible-sounding witness, even if down the road he turns out to be mistaken or lying, can be enough to give a police officer probable cause. Once the officer has that, it is not his duty to go on a search for truth. It is a jury that does that if the case gets that far. He is free to make an arrest.
So here, from what you said, someone called 911 and reported that you hit a car. It's possible that whoever called from the bar got your plate number wrong. Or you could have been the victim of a cruel prank of some kind. I couldn't possibly know that. What I do know, however, is that the 911 call reporting an accident could be sufficient to give a police officer probable cause to find you and arrest you, even if you were no longer in your car and driving at the time the police officer arrived.
I understand that as a case, there are all kinds of problems for the state and fortunately, you appear to have been able to clear your name and your license. But again, the 911 call would give the officer grounds to come looking for you.
However, if you're also wondering whether you may have a suit against the police or the caller for a false arrest, it's worth talking to a civil lawyer and looking into it. For you to have won an administrative hearing at the DMV means there was a legal finding that the officer didn't have a sufficient basis to make an arrest. That might be helful