'Differ with' v/s 'Differ from'

Is this sentence correct?

John differs from his boss on the usefulness of the business restructuring strategy.

A lot of you might think that the sentence sounds correct, specially those of you who think 'differ from' is the correct idiom; the sentence is in fact wrong as the correct idiom here would be 'differ with' and not 'differ from'.

Rule: Use 'differ from' to imply 'unlike' (as in one thing differing from the other) and 'differ with' to imply 'disagreement' (as in differing with a point of view).

Examples:

1. No one can tell how the two cars differ from one another.
   
   
2. The two political parties differ with each other's ideologies.
   
   
3. How is the book different from the movie?
   
   
4. The director differs with the producer.