Is it a bad practice to catch ‘Exception’?

I recently encountered an organization that religiously enforces the Checkstyle IllegalCatch rule (reference here) and mandates following it for all production code.  This rule seeks to ensure that developers don’t catch Throwable, Exception, or RuntimeException directly. The assertion is that it is always a better practice to catch more specific exceptions.  This rule seems a bit draconian to me, so I did a little surfing to see what others thought.  It seems the question...