Last time I looked in the rule book, the "tie" does go to the runner. Doesn't say it but specifically but it does say for an out the runner/base must be tagged before they reach the base. "Before" is not the same as "at the same time". Of course some will say that's not possible, there's never a real "tie". Within the limits of human perception there is. Best description is in FED rules
under batter is out - D3K stuation. Don't have my rule book with me, but look it up.