Pretty much nailed it on the head... But I still (would like to) believe there is a difference between 'synchronicity' and meaningless coincidences. It's an interesting subject to think about, if anything.
There is. Meaningless coincidences occur everywhere. The brain has to screen them out, or people would be doing lethal things all the time, under the misguided belief that a coincidence that allowed the person to do the lethal thing and still survived, showed that that thing is safe to do.
When people believe in meaningless coincidences, we know that it's because they have reasons to ignore the sensible thing, and consequently are risking their life. They want to believe in the coincidence. They NEED to believe in the coincidence. If they didn't, they wouldn't take the risk. So, we can already see that when this occurs, the subject would have to show an uncontrollable urge towards aberrant behaviour that justifies an aberrant belief that makes them feel good, in a way, that if that belief were removed, then in all others they would be OK, but in that person, even the mere suggestion makes them act like they'd have a nervous breakdown if they even considered the option.
Likewise, there are reasonable correlations and reasonable causations, that some people claim are meaningless, when the data is overwhelming. Those people are taking the same stance as the first group, only there, they are claiming a positive assertion, that a correlation exists where none does, while here, they are claiming a negative assertion, that a correlation does not exist where it does. Other than that, the delusion is the same.
When someone is interested in synchronicity, then they're not too bothered in meaningless coincidences. There has to be more to the syncrhonicity that a possibility. It has to have enough probability to be as likely as something else that you personally accept exists. For the person to not be suffering a delusion, then it has to be something that they could handle not being true. That means that if you could convince them that the thing isn't true, they'd APPEAR to have a meltdown. But the next day, they'd be getting on with their own lives. Like if you convinced an ENTP that all of logic and science was wrong, and the next day, he's off exploring something else. Then you know that when he thinks about such an issue, he can handle it being untrue, and so has the capacity to be objective.