The comets do not orbit the sun, they are in orbit about the Earth, and their positions are describable relative to the Earth. The Earth lies in the plane of their orbit.
I'm no astronomer, but that doesn't pass the smell test. Comets have orbits with very long periodicity, and swing so far out into the solar system, that they can take nearly a hundred years to cycle.
It's utterly counter-intuitive to think that a planet as small as earth has enough gravitational force to entrap such an object. But the sun? Absolutely.