the histogram on the back and the RAW file in Capture One match exactly if you set the so called "film curve" in Capture One to "linear response"
This is a bad sign. I don't know C1, but I guess it does not display the raw histograms.
You can test this: shoot the very same scenery with vastly different WBs, like incandescent vs. fluorescent. If the displayed histograms change, then they are past WB application, thus not representative of the raw channels.
It is important to understand, that linear vs. color space curve histogram changes how far the histogram reaches at a certain level, but it does not change when it arrives at the right edge and indicates clipping. For example the linear histogram ends at the middle of the range if the exposure is 1 EV under raw clipping; the sRGB histogram is much farther to the right at the same exposure. Increasing that exposure by 0.5 EV expands the linear histogram to the 3/4 point, the sRGB histogram changes only a bit - but they both indicate clipping at the same exposure.
Both the WB application and the color space conversion affect the appearance of histograms a lot, no matter if linear or not, and both are rendering the histograms non-representative of the raw channels.