Negligence. If they have an established criteria and did not apply it correctly (or ignored it altogether) there is a negligence claim.
Susan Haywood was left off the 2004 Olympic team in mountain biking because USA Cycling did not credit her with points earned in a race and as a result she missed the team selection. She was awarded $300,000 plus legal fees ($18,647.14). The judge said that the fact were not in dispute and issued summary judgment.
IF (and I say IF) the system here is that the fastest guy goes (I'm sure based on best times within a window), and they don't send the fastest guy, the case is easy pickings. However, it very well may be much more complicated because of language in the selection criteria that could give them much more latitude to "pick" a runner.