The clinical gaze and detachment are indeed the same. The practising doctor sees so many patients that emotional attachment is worn away quite quickly, and for the good, for a calm steady hand is better with a scalpel, and facts reviewed without bias yield better outcomes.
The near paradox in Buddhism is achieving detachment while maintaining compassion (karuna) - one of the four sublime states. Translating this back to the clinic, this is the calm doctor carrying out the work of caring. Almost caring without caring, demonstrating a higher and lower level of involvement.