Ed, tungsten illumination is rich in the red region of the spectrum, less so in green and even less so in blue. Therefore, to achieve a so called neutral with nothing else intervening, the red speed is slower than green which is slower than blue. The blue speed must be fastest to make up for the low blue emission of tungsten illumination.
This is good, because color negative papers have no yellow absorbing layer to protect the cyan and magenta layers from punch through of blue light. You see the cyan and magenta (red and green sensitive) layers are sensitve to blue light as well as to their primary region of the spectrum (red and green of course). But, since there is still a bit of punch through possible, the blue and green speeds are jacked up by the amount of speed equal to the punch through (about 50R worth) so that the filters in the beam remove the last residual element of punch through by knocking back this excess speed.
In addition, since a color negative is going to be printed, and it has an orange mask, that amount of extra speed must be added to the blue and gree layers to offset the mask. (you can observe this by contact printing a perfectly balanced negative - you will see that the border of the negative reproduces as a light gray due to this effect.)
In actual fact, the fundamental speed of color negative papers is judged by the speed of the cyan layer and the other layers are adjusted upwards from that point to achieve the goals above, namely 1. Approximate neutral from tungsten light, 2. +50R to remove any vestige of punch through, and 3. B and G speed bias approximaely equal to the dmin mask of average color negative film.
In practice, the Cyan (red sensitive) emulsion therefore uses a 0.1 - 0.2 micron grain and the Yellow (blue sensitive) emulsion uses a 1.0 - 2.0 micron grain that is nearly film speed. Since we distinguish yellow detail poorly, the grain caused by this size difference is not easily seen.
To see these effects, look at the wedge spectrograms of color paper published on the Kodak web site. The last time I looked, it clearly showed the Cyan and Magenta contamination of the Yellow due to punch through that is eliminated by appropriate filtration. If this is not done (ie by using cyan filtration) then this punch through can begin to show up in your prints. As you say, there are many reasons that one might need cyan filtration, but this does not mean it is what was intended by the manufacturere for optimum results.
So, the piece of film is a piece of negative color film, processed but unexposed.