I completely agree with Peter. In addition a would propose the vision of a supervisor as an authentic team leader, and not any kind of leader, but the one that can answer to the definition of transformational leader, or authentic leader or conscious leader; although the three of them have overlapping characteristics, conscious leader is the most inclusive in traits/skills .
Any of those leadership definitions include the traits/skills Peter talks about, but these leadership styles give another traits related to interpersonal and intrapersonal skills that are key for a productive medium and long run research work relation and are also the only way to manage mature team works.
Althoug scientific literature gives plenty of information about these kinds of leadership, to simplify, many of these traits/ skills are related to Emotional Intelligence which at the same time is very related to a Mindful way of working and relating to others, implying an open mind to others perspecives, an open heart (empathy) and an open will to what the own source of creativity makes to emerge . Theory U of Otto Sharmer, from MIT explains it in a fantastic way.