No one comments on the fruit images? The thing about skin is that a lot of times we want to see it smooth and uniform, so maybe dslr's help?
I agree with at least half of that.
"good skin tone" is a combination of many technical factors. Rolloff, color accuracy/placement, color uniformity, and tonal transitions are all very important in the final look of skin.
These factors were played with in the chemistry of portrait-oriented films for decades and are played with no in a combination of sensor (CFA, IR filter, and inherent spectral response), profiles, demosaicing algorithms, and software tools/sliders.
The rolloff into highlights is very important as, regardless of lighting, many people find skintone more pleasing if the shoulder of reds in the skintone range are more gradual. This is a large component in the Leaf Portrait profiles, which I've found nigh impossible to recreate with any other camera using any profiling software (the color engineers at Leaf are clearly lightyears
ahead of my novice level of color profiling and profile manipulation).
The color, and consistency of color is another factor. What the ideal skin color is for any given model/shot and how aggressively surrounding colors are moved toward that color are personal choices and a matter of personal/cultural/business aesthetics. It helps if the underlying system is capable of seeing the difference in a large variety of subtle colors so that if/when you want to smooth those colors out it can do so with better smoothness (color range feathering) and with less artifacts (e.g. cross over colors in shadows or bands of poor color in shadows). Both Phase One and Leaf provide a variety of very well made portrait profiles that provide for a certain amount of this color uniformity in skintones (reducing the difference between good skin and a blemish or path of overly-olive or overly-magenta skin) but importantly Capture One provides a tool in the Color Editor which (while not very intuitive) provides for a very nuanced control over this effect (usually you'd do this for a few images to your own tastes/needs and then save presets or ICC profiles which you would then use during/after shoots).
The tonal gradations also matter a LOT especially as the contrast of the light goes up. For instance a lower quality imaging chain may produce a "hard break" in skintone transitions from highlight to shadow. Software is part of that chain and in my (biased) opinion Capture One does by far the best job of making the best of those transitions for any given camera system. If the transitions are abrupt, fall on a visible line rather than along dithered and stochastic area, show color non-linearity (e.g. a shift from red to green in the shadows) then the overall effect of the skintone will be greatly harmed.
None of these factors can be effectively discussed in isolation, nor can software be discounted as each software package handles all of the above a little differently (in the case of Leaf Portrait Profiles in Capture One - a LOT differently). The skintone of an imaging system (lens+camera+lighting+software) is a complex thing and a good deal of it is subjective. But the inherent complexity is one reason to use a system that produces the results you find most pleasing with the least post-processing or tweaking - otherwise you'll be fighting to isolate and control the many underlying variables rather than simply enjoying good skintone.
And all the more reason you should test a camera system you plan on buying into in situations and manners which are relevant to your actual intended usage.
edit: I didn't even mention lens, but yes that absolutely matters too. The way detail is rendered (high frequency), transitions are rendered (low frequency), bokeh (out of focus areas), and color rendition are all influenced by the lens and any filters used in front of it.