Good question! The approximation is that electrons only interact with other electrons on the same site. But you can't put two electrons with the same spin on the same site because of Pauli! So the only interaction term you can have it spin-up to spin-down. If you considered a longer range interaction (neighboring sites) then there would be same-spin interactions as well.
I like this question. I might add a footnote to the book in the next edition!