Being a good project manager (or programme manager) entails a lot of knowledge, plenty of physical and psychological effort, precision, and so on. In truth, a well managed project/programme entails training the project people at all levels: first come the executives, then the managers (and project managers in the case of programmes), then team leaders, … More Sound Project Management is very Demanding
Tell them projects need a tailored organization, therefore they should take people from different departments (what are departments there for, otherwise?). That means the project/program manager needs the executive’ authority. Project management is a discipline, therefore it makes no sense to split it between IT and other sectors.