I have to agree with Jack that the ice cream example is flawed. I think the authors had in mind an argument that if (p -> q) and (q -> p) are true, then p and q are logically equivalent. I don't see how that would relate to modus ponens. The example is unfortunate. I wouldn't go as far as Jack has and generalize that one should not take seriously anything the authors have to say about proof.
The Editorial Panel of the _Mathematics Teacher_ seems to recognize that the role and nature of proof in a Standards-based curriculum merits reexamination. On p. 174 of the February 1997 issue, there is a call for manuscripts addressing the role of proof. A Focus Issue is planned for fall 1998. The call contains 15 questions that authors might address. Those with ideas on proof in secondary school mathematics should consider writing for this issue.