First - those who say "there are no ties in baseball" are simply reciting a platitude. There are ties everywhere in the known universe and the laws of physics do not cease to exist on the baseball diamond.
In every instance involving 2 different events there are 3 different things that could happen: A occurs
before B; A occurs
after B; A and B occur
at the same time (a tie). Even though there are 3 possibilities, the rules of baseball give you, as an umpire, only 2 choices: safe or out. In THAT sense, there are no ties in baseball.
However, if you define a "tie" as the equivalent of "too close to call", an ESPN study determined that in MLB there is, on average, at least 1 play every 6 games that is too close to call
even with the aid of instant replay!
So while you can argue whether the OBR states that ties go to the runner (it does), and you can disagree on how to make the practical decision on the field when a play is too close to call, it is indisputable that there
are ties (plays too close to call) in baseball.
As proof positive, check out the last 40 seconds of this video:
YouTube - Goofy "How To Play Baseball" 