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I guess the best we can say then is that D&L introduce a very bad model and then demonstrate that it doesn't fit the data.
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Yes, it's a strawman.
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I'm not sure that they intended it to be a 'correct' model
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They say "the best we can do", so I'd say that they simply didn't know better. I'm convinced that this section would look quite different if they'd write it today.
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The disagreement appears to be just how incorrect it is, yes?
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Of course. D&L claim incorrectly that the "Doppler/SR interpretation" is ruled out by 23 sigma by SNIa observations alone, I (we) say it's ruled out by ~3 sigma. Taking other observations into account, I think we're rather getting back to 23 sigma.