I have heard that a rainbow is...

There is truth to this. Rainbows are the reflection of the sun on water droplets in the air. On the ground, you can see only those droplets extending to the horizon, hence the bow. The higher off the ground you are, the more of the horizon, and thus the more of the rainbow, you can see. If you’re in an airplane, you do in fact see a circle, with the airplane’s shadow in the center.