Ruari,
Good question, the reason why JWs say that is because we are experiencing all these problems (violence, disasters, crime and so on), on such a widespread (worldwide) basis. If you look at statistics (don't listen to crumpet, she's clueless, I work in this field, I study crime for a living), you will see that events are occuring differently today than let's say 50 years ago. Previously we used to go through many disasters, but they weren't as frequent and as widespread as they are today. Crime is escalating at an alarming rate. For example, statistics show that in High Schools rape has more than tripled in the past 50 years.