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    $\begingroup$ TracePrint[(* charting function *), ChartElementDataFunction[_], TraceInternal -> True] quickly reveals not a few secrets. $\endgroup$ Commented Nov 12, 2015 at 5:16
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    $\begingroup$ @J.M., if you don't write that up as an answer, how am I supposed to give you your bounty? :) $\endgroup$ Commented Nov 12, 2015 at 5:20
  • $\begingroup$ It doesn't always work, you see: TracePrint[PieChart3D[{1, 2, 3, 4}, PlotTheme -> "Marketing"], ChartElementDataFunction[_], TraceInternal -> True] so I left it as a comment. $\endgroup$ Commented Nov 12, 2015 at 5:23
  • $\begingroup$ @J.M. Got it. Still a good start, though. $\endgroup$ Commented Nov 12, 2015 at 5:24
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    $\begingroup$ For "Marketing", this works: ChartElementFunction /. Charting`ResolvePlotTheme["Marketing", BarChart3D]. For some of the other plot themes this doesn't work, but the previously presented approach works. I don't know if there's a situation where neither will work, but this at least reveals some inconsistency in internal handling. $\endgroup$ Commented Nov 12, 2015 at 5:36