Actually....yes....brightness can affect saturation. If you think about it, as you approach pure white or pure black, saturation MUST decrease. For example, you can't have a pure white color that is also a highly saturated red. That is an "impossible color", at least from a human perception standpoint. You can define such a color in L*a*b* color space, but it will display as something other that a pure white / highly saturated red. The same thing happens as you approach black....the chroma (or saturation) diminishes. Saturation usually max's out somewhere in the midtone region, and adjusting tonality from that point toward either white or black will reduce the saturation that a given color space can display.
A darker image often appears "richer" and more saturated. Of course, it depends on the tonality of the pixels you are looking at. Lightening a very dark image can increase saturation, and darkening a light "washed out" image can also increase saturation. This is largely a human perception issue. If you have a CMYK color that is 100C, 100M, oY, 100K, I guess you could say that is a very saturated Dark Blue, but when you look at it printed on a sheet of paper, it is a deep, rich black, not blue. If you take out the black component, now you have a dark blue. At what point does dark blue become black? It is a human perception thing.
In RGB terms, the most saturated red you can achieve is 255R, 0G, 0B. The only way to make this color lighter is to increase the green and blue components. As those two components increase toward 255, you invariably move toward white, with a resulting loss in saturation. You can observe this in the Photoshop color picker.
I remember a photo I took of bright autumn foliage on a brilliant October day in late afternoon. The leaves were backlit. I wanted to portray that bright scene with light, shadows, and the dazzling colors of the red and yellow leaves with the sun shining through them. It's a difficult challenge on an RGB monitor, and doubly difficult in print. The dynamic range and color gamut of the real scene greatly exceeded what both the monitor and printer were capable of delivering. I started by making the highlights as bright and the shadows as dark as possible. Unfortunately, this lightened some of the reds and yellows, and consequently, I lost some of the intense color saturation that the picture was all about. There was no perfect answer to this problem, but I finally sacrificed some brightness to achieve better color saturation and found a balance that worked for me. That is a perfect example of what you are talking about.
BTW, I find 90-100 cd/m2 to be about right for good monitor to print matching. I use 90 cd/m2, 5200K, and 2.2 gamma.
Thankyou lou, what a mouthful though, had to read it twice. But that all made sense anyway. Thanks