I absolutely agree Dan. There are three "root causes" to the issue:
1. Decisions made at capture that underexposed key parts of material that is naturally quite saturated. This caused loss of shadow detail in the captured material and moved the data into a range where it is close to the hull of the colour spaces, especially the Adobe RGB and sRGB ones.
2. Converting to a narrow (or medium) colour space without making mitigating edits (increase lightness and decrease saturation) ended up pushing more material out of gamut. In a workflow where part of the work is done in a parametric editor / raw converter and part is done in a pixel based editor, this can be considered a separate step. The separation is less clear in a tool like Capture One where both types of edits can be made at the same time.
3. As you pointed out additional edits that increase saturation and decrease brightness move even more material into where channel clipping occurs.
When Ted asked in #19 if I agreed that this was a saturation issue, I hesitated to agree because that really identifies the symptom rather than the problem. I would have been just as "correct" if I had said that is a rendering intent issue or an out of gamut issue; both are equally correct answers but not terribly useful to the reader.
Ignoring the exposure issue, it is a saturation issue because of the way that the relative colorimetric rendering intent works. This rendering intent brings all out of gamut values to where they just come into gamut, so one of the channel values will be set to 0 for all affected colours; giving a saturated value. The perceptual rendering intent redistributes all of the colours that are out of gamut, which effectively reduces the colour values sitting at the hull of the colour space. For the reasons Ted points out, this is not an option for on-screen display, but is restricted to preparing images for print.