There is a lot to like about what they're doing at Swedish Covenant and at other hospitals that understand the important role of cleaning crews. Beyond the obvious and positive effects that this has on decreasing HAIs, there is also the effect that this engagement has on the employees themselves and how they view the job that they do and the place where they work.
Everybody wants to think that their work matters. Good things happen when supervisors take the time to explain to their cleaning staff that what they do can greatly affects the lives of patients. When mistakes are seen as opportunities to improve instead of failures that must be punished, employees will try that much harder.
Staff will respond when they understand what's on the line, when their opinions are asked for and acted upon, and when they are given the tools they need to get the job done.
That sounds like engagement to me.