I think the choreography is a collaborative effort. The choreographer lays out the 'shell'. The coach observes and adjusts - especially, if the skater begins to have difficulty with a particular element. The skater must put in the extras that makes it their own - the emotion, the 'understanding' and 'interpretation' of the music.
When MK was working with Lori Nichols on Salome, Lori said she asked 'how would you skate to this segment'. MK responded 'Well, Brian would do this, so-so would do that, etc.' Lori taught her to do what 'Michelle would do', instead of copying everyone else.
A lot of skaters can skate the moves, but only the champions can bring a different undefinable aspect that elevates them above others. Some find it from within (MK, Sash, Kristi, Brian); others are inspired by a special someone (i.e Angela N's relationship with coach Elena T.). Others have the talent, but lack inspiration (ie. Amber Corwin, IMO).