>It strikes me that the organizations that can't update to the latest JRE are the really large enterprises still running IE6 and so on.
Not necessarily. I know quite a few companies that have stabilized their code against a particular version and lack the manpower and/or the money to constantly upgrade and deal with the newly introduced bugs in newer versions. They usually do the upgrades on a schedule (eg. once a year or every 18 months).
For most major deployments changing to a new version of the JVM is a non-trivial task.
edit: added a life-cycle