Thank you very much, Brett. If I understand you, and in re-reading the docs, if ParallelAxisPlot is given a list, it expects each element at the top level to be a list of n-dimensional points. Following this, I modified my data so that each element at the top level contained a list of exactly one point. This does exactly what I wanted:

transformedData = List /@ data;

pPlot2 = ParallelAxisPlot[transformedData, PlotRange -> All, 
  AxesLabel -> header, PlotLegends -> cameras, ImageSize -> 300]

And I do believe I see the rationale for this approach. Each list of points can represent a set of data. And sets of data can be compared.

RadialAxisPlot and ParallelAxisPlot, are conceptually very similar, but in practice tend to be used differently. Radial plots are generally used with relatively few points[1] to make direct comparisons between them. Parallel plots are used with more points to detect clusters, trends, and outlying cases.

RadialAxisPlot's documentation emphasizes using it with either a single point, or a list of points, which then each get their own styles. ParallelAxisPlot on the other hand is documented to work with a set of points or a list of sets of points, and the styles are done per set.

[1] By "point" I mean an n-dimensional point, which is visualized as a polygon or line by the respective functions.