In general, children and young adults often do heal more spontaneously and faster than older adults. This is true for many illnesses and injuries. The military has a unique ability to see what works best since there are many ACL injuries in the line of duty.
Not only that, but the military has both young and older adults. According to a recent military study, there are slightly more adults who have the surgery after ACL injury (58 percent) compared to those who don't (42 percent).
Long-term follow-up of these cases showed more re-injuries in active duty personnel who didn't have surgery to repair the ACL. Younger adults were more likely to reinjure themselves later. The authors of the study think this may be because younger adults are more active.
All indications are that your doctor's advice is good. The chances of reinjury are greater for young, active adults who don't have the ACL repair.