Arnal questions the historicity of three key events in the life of the historical Jesus: his baptism by John, his tantrum in the Temple, and his Passion ("suffering"). These events are "key" not simply because they are normally understood as watershed moments in the life of the historical Jesus; they are "key" because they are almost (almost!) universally accepted as historical. But Arnal's argument isn't just that these three events were fabricated by Jesus' followers after his death (though he does argue this). Arnal goes further to offer "a general point about the narrative tradition in the Synoptics":
I believe that a reasonable case can be made that the stories developed out of motifs in the sayings tradition. Sanders very much to the contrary, the narrative tradition can be understood as a result of a narrativization of themes already present in the sayings tradition, as interest in Jesus as a teacher modulated into a desire to make Jesus himself a champion and paradigm of the community ethos generated by those sayings. (Arnal 1997:215; emphasis in the original)
Anyone familiar with the history of the historical study of Jesus knows that the distinction between the sayings and narrative traditions has played a storied role in the historical Jesus scholarship. The so-called "third quest" has largely privileged the narrative tradition (see Arnal's reference to E. P. Sanders, above), though I get the impression that some third-questers try to remove the distinction rather than invert it.
Here, however, is my problem with Arnal's argument (and with any Jesus historian who privileges the sayings tradition and actively derides the narrative tradition). Arnal offers his "reasonable case" that the narratives he examines arose from motifs in the sayings tradition, but nowhere does he justify the bifurcation between sayings and narratives in the first place. What historical basis does he have for presuming that Jesus' earliest followers preserved/passed on his teachings but were uninterested in narratives about him? Additionally, what historical basis does he have for assuming that, once Jesus' followers did develop an interest in stories about Jesus, they didn't have any and so had to turn to what they knew from the sayings tradition in order to fabricate some?
I know of two usual answers. First, Jesus' sayings are demonstrably more similar across the three synoptic Gospels (Matthew, Mark, and Luke) than are the accounts of Jesus' actions. Some historians (not necessarily Arnal and/or the Jesus Seminar) have used this empirical observation to justify the bifurcation between sayings and narratives. Second, and more importantly, a number of scholars, mostly associated with the Jesus Seminar (and here I would include Arnal) privilege the sayings source, known as "Q" (= material that appears in Matthew and Luke that does not appear in Mark), in their reconstructions of Christian origins. Since Q largely comprises sayings and not narratives, the assumption is that Jesus' earliest followers (or at least a subset of Jesus' earliest followers) cherised his teachings and had little or no use for stories about him.
Even leaving aside the hypothetical nature of the so-called Q-document, this second point rests on some dubious assumptions. First, it assumes that the Q-document, assuming it did actually exist, corresponds to the theology of a specific, identifiable group of Jesus' earliest followers. Second, it neglects that Q as currently reconstructed does indeed contain a number of narrative features. Third, again assuming that a Q-document actually existed, it assumes that reconstructions of that document from the material in Matthew and Luke give a reasonably accurate portrait of the Q-document. Joe Weaks's PhD dissertation, "Mark without Mark: Problematizing the Reliability of a Reconstructed Text of Q," should convince us to put such confidence behind us.
In sum, the choice between sayings and narrative traditions in historical Jesus research is a lark. Neither is epiphenomenal of the other; both were of utmost importance to Jesus' earliest followers. Jesus was remembered as an authoritative teacher (so Mark, passim) whose halakha put Torah into proper perspective (see, e.g., Mark 7.1–23; Matt. 5.17–20; Rom. 3.21–31, among many others). But he was also and simultaneously remembered as a powerful prophet/healer/exorcist, whose words calmed the seas, cast out demons, and silenced his enemies (e.g., Mark 1, 4, and 5). Any reconstruction that privileges the sayings over the narratives or the narratives over the sayings has already started off on the wrong foot.