The circumstances that produce a Rock Paper Scissors finish in a cross country race are unusual enough that each case gets its own moment of social media attention when it happens. Two runners build a significant lead over the field — large enough that the gap to third place is insurmountable regardless of what the leaders do. They've been running together long enough that the race between them has become something other than competition in the standard sense. At some point approaching the finish, by apparent mutual agreement, they slow to a jog, face each other, and throw.
The 2010 Golden Horseshoe meet in Ontario is one of the documented examples: two training partners who had lapped the field decided to let the game determine the result rather than damage a friendship with a final sprint. The winner stepped across the finish line first. The race continued and concluded. Neither team was disqualified, though opinions about whether this was acceptable sportsmanship varied depending on who was being asked.
The rules question is genuinely complicated. Most race rules require continuous forward motion and prohibit deliberate non-competitive finishes. Whether a three-second pause to throw Rock Paper Scissors constitutes a non-competitive finish depends on how strictly the officials interpret "competitive" and whether the outcome itself — one person crosses before the other — satisfies the race's technical requirements. Timing chips decide placement, so the question is whether the method of determining order, rather than the order itself, violates the rules.
What these finishes have in common is that they happen when the competitive stakes for the two leaders have already been resolved by the size of their lead. The race against the field was over. The race between them was, at that point, a formality. Rock Paper Scissors is one of the faster ways to resolve a formality.