There is no reason why the prime minister's challenge to the professions—to break down barriers between professions—should not apply to public health, which more than many parts of the NHS needs effective leadership. This should be provided by the person with the most appropriate skills, experience, and personal characteristics. The possession of a medical degree does not necessarily or automatically confer these benefits, although it undoubtedly is an important part (although not an exclusive one) of the professional toolkit.
The type of special pleading that suggests that only one professional group can lead is rapidly disappearing from many parts of the NHS, and rightly so. If public health wants a better profile than the one it often currently seems to have it should make best use of whatever leadership resources it has, rather than fight internal battles about who is in charge.