Although the consequences of doctors mixing the personal and professional can clearly be devastating, the same idea applies, to some degree, to any position of authority. It can be difficult to teach a family member a new skill, for example, for fear that corrections to technique will be taken as personal criticisms. Similarly, being a friend's boss can put a strain on the friendship. Performance reviews, the use of sick days... sometimes it's easier not to know all the details of a co-worker's life.
In any case, Wilson's refusal to believe cancer was the cause of his friend's new symptoms shows that sometimes a little distance is necessary to see things clearly and do what has to be done.