According to the Washington Prowler the idea for the Edwards’ call came from Coulter’s publisher:

After booking Coulter, MSNBC producers reached out to the Edwards campaign. “It was an easy decision,” says an MSNBC associate producer. “It was the idea of Coulter’s publisher to do it.”
The call was made to the Edwards campaign by an NBC — not MSNBC — producer, says a source familiar with the arrangement. “Mrs. Edwards was told what time we’d be calling, and what the questions would be leading into her call. Coulter may not have known that the deal was done, but we thought her publisher had told her about what was happening,” says the MSNBC source. “This was not Mrs. Edwards idea; it was a something hatched between her, the campaign and the publisher to promote her and Coulter’s book, nothing more.”

Now the problem with this story is that we would have to believe unnamed employee of the MSM, not something I’m quick to do. I think we need one or two other unnamed sources to verify 🙂