I think that the major players in hosted/managed access control don't think of themselves as "integrators" and probably aren't well represented in this survey.
Companies that specialize in hosted/managed access (such as Kastle) are very popular with some clients, particular property management firms who operate large high-rise buildings. These companies often manage the electronic building directory and visitor management systems in addition to the access control so that when a new employee is added, they appear in all systems automatically.
I have several clients who use hosted/managed access to whom I have pointed out the great cost savings that could be achieved if they bought and managed their own systems. Often the payback period is six months or less. My arguments have mostly fallen upon deaf ears - most of these clients love the managed access concept and are happy to pay the extra costs for it.