Alright, now that we are out in the open, I'll defer the discussion of Gamma for a bit to tackle RGB balance and white points.
Picture, if you will, the CIE 1931 Gamut chart. For each standard, there is a defined location for each of the three primaries. However, for all current video standards, the same white point is used (D65, or x=0.313, y=0.329). Since the 1931 Cartesian system does not include luminance (Y), all points in the grayscale should hit D65. After all, since the difference between black and white is the amount (intensity) of light, the "color" of each point in the grayscale does not really change.
Let's emphasize the key point here: all points on the grayscale should be on D65
Think of intensity, or luminance, as being orthogonal to the xy plane.
With me so far? Alright, then there is one additional piece to the puzzle: not only does each standard have a different defined point for their primaries, but they also have a different balance to the primaries that constitute white light. This is why you just can't calibrate to one standard and think it will work for all standards. Of course, for display manufacturers, this also drives you nuts because at a fundamental level, the color of a primary is going to be relatively fixed (e.g., dichroic filters, phosphor, etc. all have one color!).
So, where does that leave us for color balance? There are two issues at play here. The first is that there is a relative mix of red, green and blue that should be maintained. Second, this mix should be maintained as close to the defined white point as possible. Unfortunately, because of the pre-defined color issue mentioned above, you often cannot satisfy both of these two goals at the same time.
So, the color balance charts in my guide refer to the relative levels of red, green and blue that are required to bring the colors into balance given the defined mix for the HD standard (Green: 71.5%, Red: 21.3%, Blue: 7.2%). Why don't I look at my absolute deviation, rather than this relative deviation? Because to me, it is more important that the colors are balanced, than that they are at the right white point. Also, I can use both the color temperature and color error to tell me how far off of D65 I am, and how noticeable it will be.
Submariners have an expression about driving a sub. Bad sub drivers "chase the bubble", and as a result, they are always putting in steering corrections based on where the instruments said you were, rather than based on where they are indicating you are going. For me, focusing on the absolute deviation is a lot like chasing the bubble. Algae in Theodin's beard bugged the snot out of me. Slightly blue snow does not.
So, back to Bob's original question: are there several mixes of RGB that will meet D65 and be properly balanced for a given standard? The specific answer is no. However, the nuanced answer is that there is an error tolerance around this (dE), and I aim to make sure the balance is correct more so than hitting the theoretical level for a primary to be at D65.
Now if that is perfectly clear, then I definitely need to pay for the second course of Alan Greenspan's Guide to Business Communications!