I don't think that is a real Japanese proverb, but it was told to me as the way of explaining life in Japan. However, I entirely disagree. Everything is personal, and everything is business here. I suppose it has a lot to do with the work hours they keep, and thus the relationships that are established between colleagues, and the family relationships that fall by the wayside.
Most people go to work at inhumanly early hours (we all know I'm not a morning person though, so maybe not so bad for others) and stay until late in the evening. For example, most teachers are at school by around 7am and then are still there at 8pm, and then they go back on Saturdays and for at least half a day on Sunday. As a result, teachers develop strong friendships with each other - as do people generally with their colleagues. These friendships are far more important than they are in Australia, in my experience, as your work colleagues become your only friends. You should be able to imagine that it is hard to maintain friendships with people who work in other places, let alone in other professions. Teachers go on trips together - usually during the summer, then again a couple of other times each year on a long weekend. They all pitch in and hire a bus, or car pool and go skiing or shopping for a long weekend.
Also, many teachers end up married to other teachers. That does mean that you have to watch what you say - I almost started complaining about 1 teacher who leaves the room when I enter (to supposedly teach a class together) but the teacher I was talking to luckily told me it was his wife before I said anything... (surprisingly, the husband claimed the wife enjoyed english class!)
Anyway, back to the topic of merging fun and work. In Japan many marriages suffer because one spouse is relocated regularly - every 3 years - teachers, judges, many bureaucratic jobs. As a result, kids can spend half their lives living away from one parent.
Actually, kids spend so much time at school that the teachers become surrogate parents. Japan used to have some pretty draconian corporal punishment rules on the books, as well as classes on Saturdays. Now the kids only have sports on Saturdays, and pretty much all disciplinary methods have been outlawed. Now teachers practically 'mother' the kid over any small infringement. Kids regularly have meetings with their home room teachers to discuss any emotional problems, and they even have a class called moral education (which is not just sex ed.)
Teachers go to the students' houses once a term to check to make sure everything is ok, and are just really involved in their lives.
So when I was told that 'work is work and fun is fun' is the Japanese way I just nodded (now that is totally the Japanese way) and contradicted them in my head.