Actually, THIS is why no two people see the same rainbow:

Poulton House Garden, Leeds, UK, 2007

Think about it: Imagine yourself looking at a rainbow. Locate a foreground object and a background object relative to the rainbow's edge, and then move to the right or left. Unlike parallax with fixed objects, the rainbow will move with you relative to the fore- and back-ground. A fixed object doesn't do that.

Now, imagine that you and your friend are standing next to each other, and one moves left, the other right. "The" rainbow will appear to move with each of you - in two opposite directions. Are you still looking at the same rainbow?

Here's what Barfield says in Saving the Appearances about the rainbow:

"Look at a rainbow. While it lasts, it is, or appears to be, a great arc of many colours occupying a position out there in space. It touches the horizon between that chimney and that tree; a line drawn from the sun behind you and passing through your head would pierce the centre of the circle of which it is a part. And now, before it fades, recollect all you have ever been told about the rainbow and its causes, and ask yourself the question Is it really there?"