They may have wanted more from the Twins than from the other teams, but with rentals, but I agree, I doubt it would have been significant. Fans care about the rivalries more than the GMs do, rental players should go to the highest bidder if you're a seller.
Of course, many years there are more than just rental pitchers available and then I do agree these teams would be inclined to keep them away from the Twins. And with the Twins in a habitually bad division, they are going to run into this scenario more often than teams with only one 'seller' in the division per year. Can't do much about that except shop elsewhere.