Why in the world would you ever rinse an oyster. I've seen it done many times in TX and rarely anywhere else. You rinse an oyster and it tastes like ... NOTHING! Or it tastes like cocktail sauce ...but it doesn't taste like an oyster!
I thought that perhaps Gulf oysters perhaps just don't taste very good and that's why they're rinsed. But then I bought and shucked some myself and discovered otherwise.
So why rinse an oyster?? If you like the taste of cocktail sauce so much, just drink cocktail sauce!