Thanks for asking this. Both the survey data on satisfaction rates and in-depth qualitative interviews point to better service delivery by many faith-inspired healthcare providers. The qualitative data suggest that this is due to staffs being more attentive to patients, more respectful, and closer to the communities. These attitudes may be related in part to intrinsic motivation, but they are also related to a positive culture and systems that faith-inspired providers have in place to encourage and train staffs to place service to patients at the center of their work. We found somewhat similar results for faith-inspired schools in Africa (https://openknowledge.worldbank.org/bitstream/handle/10986/16391/9780821399651.pdf?sequence=1).
In the work on faith-inspired healthcare providers, we did not investigate in details how the providers train their staffs to encourage great service to patients. But in a study we recently did on Fe y Alegria schools in Latin America, we looked at how the schools trin teachers to be responsive to the need of their students (https://openknowledge.worldbank.org/handle/10986/16375). Motivation plays a role, but the role of accountability and the dedication of the school's management to foster a culture of service is probably even more important.
Overall, the message is that while is not easy, fostering such attitudes can be done, and the experience of faith-inspired providers is useful to better understand how. The message of the studies is not necessarily to scale up provision by faith-inspired providers, but first to at least fund their work properly when it is of high quality (this is often not done by governments), and next to learn from their successes, and see indeed how they can be replicated in other types of schools.