The single most important aspect of any training is recovery. Like your coach, I believe in taking a break between seasons. You're not going to lose much fitness, nor would you gain much with the easy running many advocate. The physical and psychological benefits of a break will actually benefit your subsequent training.
For the record, my personal coaching recommendation has always been to take 2 weeks off between seasons. Alternative physical activity is okay during the break, but no running outside of those activities. So swimming, basketball, ultimate frisbee, etc. were fine.
Slightly off topic, but I wanted to respond to Flagpole's recommendation of training through the indoor season in preparation for outdoor. I know this is a popular train of thought, but I don't adhere to it. I don't put more value on the outdoor season over the indoor one. To me, they both provide opportunities to compete at a high level. In some regards, indoor provides a better competitive venue due to the consistent conditions - no rain/snow, no wind, comfortable temperature. It's not unheard of for someone to run faster indoors than outdoors. And the team dynamics are no different than during any other season.
Modern training theory now accepts the reality of being able to peak three times in one year. There are events, meets, and championships to be won. Why not go for it?
/soapbox