Color pallets were the main reason for picking different films. In the digital age though you can't get repeatable results, and worse-yet you can't get repeatable results when you upgrade, switch to a backup, etc. without process.
However, the skin tone comment isn't about color rendition, it's about skin tone rendition, and if you were to photograph someone from the North of England, Sub-Saharan Africa, Japan and Nepal and with a straight face say "This camera renders skin tones wonderfully!" you'd be wrong. Heck, shoot a portrait of my family, and I guarantee you won't get three pleasant skin tones out of any camera without a lot of time in Photoshop.
Even within a specific vendor, different sensors have different color ranges and you'll likely get different results even if the camera's engines and any converters are somewhat normalized. Heck, different lenses and filters make it even more of a crap shoot. A slight green or magenta cast to a UV filter or lens element can totally change the tone, as does shooting under different lighting conditions.
Just like filters on an enlarger coupled with film choices and paper choices produce specific results, control of the steps in the process allow you to produce amazing prints compared to the default baseline, similar to an automatic machine print.
If you look at St. Ansel's early darkroom work compared to prints of the exact same negatives you can see the difference between a good and a great print even in B&W. The negatives certainly didn't age into better images. Control of the process steps mean being able to take images at the same event with a Fuji, Nikon and Canon camera and within the limits of the available sensor data produce equivalent results easily and automatically.
Baseline, adjust color palate to taste and adjust white balance to taste. Lather, rinse, repeat. Then you get the rendition you want every time, no matter if it's daylight, sunset, CFLs, Tungsten...
Paul