Not in this particular case, but in general the projection type is very significant.
In this case the track to be measured is a straight line on a Mercator; and is therefore a rhumb line. This one just happens to be along a parallel of lat which means that the equation chlong x cos mean lat yields the exact answer - 268.413NM.
If the projection type had been a Lamberts Conformal then the straight line would have been along the great circle and the exact distance would have been slightly shorter - 268.263NM.
Not a lot of difference and both answers still convert to the same 309SM.
The examiners were making it easy by choosing points close together.
But to illustrate the significance of projection type, take the example of say 56N000W to 56N180W and see what a difference there is between the RL distance (straight line on a Mercator) and the GC distance (straight line on a Lamberts).
RL = 180 x 60 x cos56 = 6039NM True Trk 090 or 270, take your pick.
GC = 2 x (90-56) x 60 = 4080NM Init True Trk 360 to the pole, then 180 from the pole to 56N180W.