During their conversation, Captain Random turns into the Southern motorist who died; the implication is that that tragic event was also "him," insofar as he is chaos and randomness personified. He "controls" everything (because he is Randomness), and the tragedy of the story and the reason for the protagonist's despair is that despite that implication, everything is still meaningless because no one can understand Captain Random; as soon as you perceive him, he becomes part of the pattern; as soon as you comprehend him, what you have is no longer Randomness. It's like the worst of both worlds: God is real, but the universe is still just uncaring chaos.
If you want to insist on the non-magic interpretation of her conversation with Captain Random, then you certainly can, but the story still makes internal sense. In the first section, she harps repeatedly on how she believes what she can see and observe, how she trusts what she can interact with (if nothing else). By the end, she has "observed" Captain Random and spoken with him. You, from the outside, might say that it was likely a hallucination, but it clearly felt real to her (and she emphasizes that she checked her credit card records to confirm that she didn't dream the whole day). It's hardly out of character for her to take her observations at face value and extrapolate the same framework I described above.