As neither Johnson or Shields have long term contracts, you would only trade for them if you thought by adding them you would be contending next year. The Twins are a long way from contending unless you believe that Diamond is for real, Gibson and Baker can put in a full season., and Hendricks can be solid. You can wait out Gibson and Baker if you believe that Deduno and DeVries can hold down the spot short term. I don't think you can be that optimistic. IMO Span is the only player the Twins have that you could call established that they can trade for some pitching. In the long term, the Twins would be better off trading him to a team that has some pitching depth for a B+ pitching prospect or two. Trading for Shields or Johnson is a bandaid at best. The Twins need more than a bandaid.
Pursuant to the "Rule of Zach Parise", Josh Johnson will obviously force a trade to his hometown team, and coerce another pending FA to join him!
Agree with your take though, even if the "rental player" status (plus the fact that the Marlins get destroyed in virtually every trade they make) keeps the price down, why would you do that if you're the Twins? Payroll's going down, not up, and even for one year, that would be hard to swallow, given the fact that we arguably need 3 OK starters more than we need one good one.
As much as guys like Joe Saunders kind of suck, you could stitch together an argument that it would make a bigger difference in the win/loss column adding 3 serviceable guys like that, versus one upper-end guy (like Grienke or even Sanchez) and then having to fill out two other spots with Cole DeVries, Blackburn, or another random AAA starter because you're out of money. Plus, those guys won't sign here, and we won't offer enough years to get them.