The exact meaning of 'directly' isn't defined in the rules (I think). Imho, one valid interpretation would be to use the definitions used in the description of 'Pull, Push, and Slide'. I.e. you are moving directly towards a target if each of your steps move you one square closer to the target.Ohhh man... when I heard you were in the hospital I came directly here without delay!
All those buildings, women, children, cars, busses and street signs he ran over in order to go "directly" to the hospital are certainly not happy that he came "directly" to the hospital.
Note, that I'm not saying that it should be interpreted that way - just that I would say it is a valid interpretation based on the 4E PHB rules alone.