If you think about it, them having each one a fast lap is almost necessary to a triple tie. If that weren't the case, you would need certain combinations of ties between the nine lap times to make the triple tie, which is a lot more difficult. For example, with the first runner having the fastest first lap and the other two tying the second and third laps.
I wish there was a way to watch three different ghosts at a time in this game like in CTGP for Mario Kart Wii, that would make these so much better imo.