Short answer: Yes.
Long answer: At least as far as glycogen is concerned, it probably doesn't matter for the vast majority of people who do moderate exercise once a day. However, protein synthesis is also increased during the refueling window, and everybody can benefit from that.
It's well established that calories get turned into glycogen more quickly if consumed shortly after a workout. The American College of Sports Medicine's 2009 Position on Nutrition and Athletic Performance has this to say (emphasis mine):
Timing of postexercise carbohydrate intake affects glycogen synthesis over the short term (110). Consumption of carbohydrates within 30 min after exercise (1.0-1.5 g carbohydrate·kg-1 at 2-h intervals up to 6 h is often recommended) results in higher glycogen levels after exercise than when ingestion is delayed for 2 h. It is unnecessary for athletes who rest one or more days between intense training sessions to practice nutrient timing about glycogen replenishment provided sufficient carbohydrates are consumed during the 24-h period after the exercise bout. Nevertheless, consuming a meal or snack near the end of exercise may be important for athletes to meet daily carbohydrate and energy goals.
The 1996 study they cite to back up that bolded section doesn't really make that claim, except for this bit in their discussion:
...it is considered that the major benefit of consuming carbohydrate in the immediate recovery phase is to promote earlier recovery rather than exploit a period of increased glycogen storage rate.
OK, fair enough. Anyone working out one hour a day will be probably be burning 500-1000 calories. The typical human has 1500-2000 calories worth of glycogen stores. Unless you're starving yourself the rest of the day, those stores will be replenished by your next workout no matter how slowly you're synthesizing it. The "glycogen restoration window" is only really significant for athletes who want to turn around and do another workout a few hours after the first one.
But protein synthesis also slows way down after the refueling window. This 2001 paper in AJP (titled "Postexercise nutrient intake timing in humans is critical to recovery of leg glucose and protein homeostasis", in the American journal of Physiology) has some nice charts of protein turnover in the leg when refueling early (right after exercise) or late (3 hours later). This one shows that late refuelers actually have a net loss of protein in the short-term once you account for protein lost during exercise.
Clearly a net loss of protein is not optimal recovery. I don't know where the "60 minutes" number came from (or 90 minutes or 30 minutes or whatever else the people on triathlon forums are throwing around these days). But there is a definite benefit to recovery from having your meals sooner rather than later after your workout.