I fear I may be venturing again into "just because" territory, but this one bugs me.
We all know that you usually use いる (as in not ある) to refer to living things, as in 私は日本にいる（△ある）. Yet it is acceptable to use ある in the sense of "some" when the specifics are not important, so it's acceptable to say both ある日, for example, as well as ある人. ある人はそう言った。
Is there a reason for this, or is it just an extension of that usage of ある (in which case why isn't it いる人)?