Joking aside, if I’m seeing more than one of these hypothetical professions, someone needs to coordinate my care. For myself, I trust me to keep everyone informed. Anyone else wouldn’t have the same incentive to do a good job. After all, I’m the one that suffers the consequences if there’s a mistake. :)
Well, going by our nomenclature for other things, the hypothetical leader of the other practitioners, by analogy to a leader in the army, could be called a "general practitioner."
All it takes is one accident or affliction to change this ability. Unresponsive due to a car accident, for example, or simply not having your list of information when you got rushed to the hospital. Confusion due to a high fever. A stroke due to an undiagnosed and hidden condition. Heck, simply age or winding up with a complicated health situation can do it.
In short: You really only can trust yourself if you have enough luck.