Anyone can come up with three bad things happening at a time if you look hard enough. Say you get into a fender bender. If you look at the morning before you left, say you forgot to wash what you wanted to wear that day and you misplaced your keys. Would you have thought the first two things, the clothes and the keys that bad if you hadn't had the accident? I think for some it is just a trigger to let the bad thing go so that can start to focus on the positive.
I do not think bad things happen in threes. This saying was used in mystery book especially the Japanese articles, and most people consider it is a superstitious thing. People use it if three bad incidents happen at ago.