Sure, you need to be individually good at thinking, etc. But the difference between 1st and places further down the ranking is teamwork.
(In a certain sense, this is actually the ideal "teamwork" setup in the industry as well, to have a bunch of people who own their part and are trusted by their colleagues take care of it and not step on each other toes than kumbaya let's all get together on the same problem.)
We were "just" three friends who had studied together for 4 years, knew each other's strengths and weaknesses intimately, and then for the comp trained intensively on optimising the "parallelization/scheduling" aspects (as you put it) to get the best score in the minimum time. That included both the logistical and mental aspects of recovering from setbacks midway through the 5 hour problem sets.
During the finals, you'd be surprised how many teams' teamwork we saw fall apart when three very smart people under intense time pressure hit unexpectedly failing submissions with the bottleneck of a single computer. ICPC is a genius format.