Like most proverbs, it came from a less-populated, relatively immobile society. It makes sense to think that in a peasant, small-town or rural environment where people stay put, you will run into people again (whether you like it or not). This would not seem to be the case in more modern times.
But wait a minute. The omnipresence of electronics and social networks has once again made this true. You can look up people from long ago and far away on the ole Web (and vice-versa). The difference being that you can choose whether to make yourself known and make contact. And if they belong to long ago and far away, they should probably stay there.