I heard they did due diligence in asking about Red Sox starting pitchers – presumably Jon Lester and Josh Beckett – but were unwilling to talk about their top minor league arms in return, which basically ended the conversations pretty quickly."
Maybe that means Arizona is no longer in the market for a starter. Maybe they're waiting for Garza to be placed on waivers. Maybe they just weren't interested in Lee or Blanton.
What's certain is the D-backs are in a good position to add a National League pitcher if they are so inclined. Arizona is essentially the worst of the NL contenders, meaning they have first dibs at any players placed on waivers, as long all the teams out of contention pass.
The only way Arizona could win a claim for an American League player like Shields, Lester or Beckett would be if not only non of the teams below them in the NL put a claim in, but also if not a single AL team did, either. For a more detailed explanation of the waiver process, check out the MLBDD Toolbox.
The Diamondbacks are 55-51 and on a four-game winning streak. They trail the San Francisco Giants by two games in the NL West and are five and a half games back in the Wild Card.