[kyleyeats]

The idea is that it puts Earth at the center of the biological universe.

Generally the idea is that abiogenesis is very rare. I don't think any panspermists are saying that it only happened in one spot. As you pointed out that's basically the same belief as thinking it happened just once on Earth. The two 'versions' (they're not mutually exclusive) I'm familiar with are spreading via waterbears on comets or whatever, and also seeding by intelligent life. I think we have evidence for both in our own solar system, although the life we've seeded probably didn't take hold for very long.