Hello, M Azingrace!
It was helpful to see your examples in response to Tom's request; I have just a moment to respond with a few quick thoughts.
But first, if you don't mind, since it well help people know what to respond to, a request for a little more clarification. When you stated
I'm reading J. I. Packer's Evangelism and the Sovereignty of God and thought it was helping to clarify, but when I read the compare and contrast chart of the two models of Arminianism and Calvinism here, I get confused again.
does "here" refer to this site (this is how I read it) or the Packer book? Perhaps you could point us to an example or two of what seems confusing.
I have been a long-time listener to the White Horse Inn, so it seems clear that you are referring to the most current (6/22/08) broadcast. I have heard the program twice, so I might be able to provide a bit of perspective.
I do not recall the WHI hosts "pick[ing] apart" the interviewed pastors' words "in order to reveral their Arminian positions"; if they mentioned the word I missed it and would be happy to know where in the program it was used. Their point, which they did state quite bluntly, was to demonstrate that it is not uncommon for contemporary evangelical pastors to employ a categorization of sin which not only does not account for all of the biblical data--specifically Romans 4 and Romans 7, both foundational passages--but also is indistinguishable from Rome's teaching at a point where Rome has strayed furthest from the Gospel.
A main thesis of the WHI is that contemporary American evangelism is largely severed from its Gospel roots. While the hosts would certainly want to see Arminian teaching "rooted out", I think they are much more concerned about rampant Pelagianism and Gnosticism. An analogy may help: a person may indeed be in danger of suffering and eventually dying from long-untreated diabetes, but diet modification, exercise and insulin injections will not be ordered right away if he is brought into the ER with a severed artery in his neck.
Finally, the main target of the WHI's "inquisition" is pastors who have been charged with preaching Christ and Him crucified but who fail in significant way to do so. This is an example of a Scripture with which I am sure you agree:
Not many of you should become teachers, my brothers, for you know that we who teach will be judged with greater strictness. (James 3:1, ESV)