Your coach probably read that Bannister ran something close to 15 miles/week to break 4 minutes for the mile on cinders -- worth roughly 3:56 mile on modern all weather track -- but that training was interval based and Bannister seldom raced longer than a mile. Bannister (like all modern day elite HS 1600m runners capable of something close to 4 for a mile) could run 49-50 for a single rep of 400m, which makes things much easier when trying for a fast mile.
Interval training also provides a stimulus beyond the actual running time, for example, if Bernard Lagat runs 20x200m 27 w/ 45" rest between, his cardiovascular system is actually working much harder on his "rest" than if he were out jogging along at a steady 6'/mile. Most folks who race all out for a 6' mile can't manage even a single 200m rep in 27. Like Coe said, at some point speed is inescapable.
60 miles/week isn't a lot of miles, but most likely your coach is trying to explain to you that not all miles are worth the same and maybe more specific training for your event, without quite so much worry over total miles run, will be more helpful.