It depends to some extent on semantics, and you have far more stamina than I for that.
My old teacher and Wikipedia both referred to Saturation as "the colourfulness of a colour relative to its own brightness". Possibly not the most technical description, but it gets the idea over to non technical folk.
The difficulty with such a statement, as eloquent as it may be, is that it leaves "color" itself relatively undefined. Color may be a highly overloaded term, but in technical terms, color is the product of three dimensions...when you take out saturation, you still have hue and intensity/brightness.
I may be playing semantics here, but I think it's important when discussing color accuracy, calibration, etc. to discuss color properly, in all three of it's dimensions. Therefor, I think a more accurate rephrasing might be: "Saturation is the richness of a hue relative to it's intensity."
Then I'd totally agree.
The rest, we agree on, basically.
If you are going to represent something in a space smaller than it occupies in real life you have to do something, I am saying get the saturation levels relative to each other as close as possible (to fit in the smaller space), get the brightness as close as possible (to fit in the reproduction medium), but there is no excuse for not getting the hue correct. If you do that, even though it isn't "true to nature", it is an accurate rendition and will appear so to the eye.
I agree. There is no excuse to not get hue correct. That's a radial factor, and it should be possible in any gamut to choose a proper hue. I still think that saturation matters to a degree. If you have a very tiny gamut, where a deep red is simply not an option, then it doesn't really matter how accurately you choose your hue...your "deep red rose" will still end up some form of pink. In terms of the difference between say sRGB and AdobeRGB, I do agree, a red rose will appear acceptably red as far as your perception goes, that you could have relatively accurately reproduced the color of your image.
I also think that this very same circumstance is the very reason people such as ourselves are constantly seeking larger gamuts...not just for screen, but really more so for print. Greens are easy to reproduce in print...it's the reds, blues, violets, magentas, and in some cases even the oranges that are so difficult to accurately reproduce in print.