I think the disagreement on this issue stems from the definitions used for paraphyly.



Apeltes: I thought a paraphyletic group was a group of species that share a common ancestor, but with some of the descendents of that common ancestor excluded.



This vague definition can render any two taxa, that are not sisters, paraphyletic. While this definition is common in texts, it is not very practical if one is interested in differentiating between the two concepts.



CKing: Paraphyletic groups are defined by symplesiomorphs or shared ancestral characters {(note: and exclude taxa with relevant apomorphies)}. Polyphyletic groups are united by convergent characters.



This allows for differentiating between the two scenarios in many circumstances, but perhaps not always, because sometimes we don't know whether traits are convergent or plesiomorphic (see my post on Sept 29).



Hopefully this helps.

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