The teams we beat trained as individuals and were selected competitively against each other as their school's "best 3".

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.