Technically, you are riht. In practice, though, it doesn't matter all that much.

As you say, we don't know where the distribution is truncated, but let's assume for the sake of argument that it stops abruptly at 5 standard deviations below the mean (which is the same as changing the lower integration limit from -Infinity to -5). This lifts Daigan to a whooping 0.318639 standard deviations below the mean. Even setting the cutoff at 3 standard deviations only lifts her to 0.315081. There just aren't enough people that far out to change the numbers a whole lot.