A conglomerate violates the definition of institution when its staff members do not interact regularly and face-to-face.
Hospital chains are the classic example of a conglomerate. The staff of one hospital rarely interacts with the staff of another hospital. Academic conglomerates may also exist. For example, Harvard University has several affiliated hospitals, and the physicians at those hospitals all have academic appointments at Harvard, but the professional staff at each of the hospitals operates independently from the others.
An expert is not just someone who knows a lot about a particular topic. We additionally require that the expert write about the topic, and be involved at the leading edge of investigation of the topic.
This definition has several consquences, the most important being that some extremely good physicians, especially some in private practice, are not counted as experts. We have elsewhere written about this in detail.
We define institution not in terms of buildings or edifices, but as a group of people who regularly interact face-to-face and exchange ideas. The implication is that a patient who is seen at one of the institution's facilities has access to the brainpower of the entire institution. Contrast this definition with conglomerate.
For most VA Hospitals, the integration of their faculty with a medical school faculty is usually a close one. So, as a matter of course, we combine the VA and the medical school into one institution.