Nature, in this context, means there is a biological predisposition toward homosexuality; and that in turn implies something in the genetic makeup.
You, sir, are simply dancing around the point. It's not clear why.
You're close. Nature, in this context, means there is a genetic component, and genetic component means linkages and associations. What confuses people is how little linkages and associations play into the mix. But it doesn't imply a gay gene exists. Yes, it's complicated.