When you are weighing the value of medals and championships, the Olympics are hands down #1. These are the ones that everyone cares the most about. Then it's world championships, Diamond League races, and national championships. But the Olympics are at the top--hands down.
Does that mean that winning an Olympic Gold instantly means you are the greatest ever in your event? No--but it becomes a significant part of the package. If you are able to peak the right way, against that level of competition, that might involve luck, but it involves a whole lot of skill, too.
The 1500m actually strikes me as an event where less "luck" is involved than other events. The reason I say this is that if you go back over championships from the last 5 years or so, you find quite a lot of repeat medallists. Typically, though not always, there is one person on the medal stand who (at least up to now) will not medal again. Check it out:
2011 Men's 1500m WC: Kiprop, Kiplagat*, Centro
2012 Olympic: Makhloufi, Manzano*, Iguider
2013 WC: Kiprop, Centro, Conje*
2015 WC: Kiprop, Manangoi*, Iguider
2016 Olympic: Centro, Makhloufi, Willis
The asterisks are for runners who, up to now, have not reached the podium since they first got a medal.
So in most cases, there is one person to medal who will not medal again--which would suggest that there is indeed some luck in the event, as there is in every sport--but the other two spots tend to go to repeat medallists, which suggests a certain "bias" towards experience and skill. Interestingly, this year's Olympic race featured a podium composed *exclusively* of medallists from prior Olympics and WCs. Other events might be more susceptible to fluctuation--I'd be interested, for instance, to see how the 800m compares. But whatever luck there is involved in championship races, there's a lot more skill\