The issue has nothing to do with bit-depth but with how much dynamic-range is shown.

RAW files record a certain number of bits per photosite. This is usually 12 or 14 bits. JPEG images offer a fixed bit-depth of 8-bits per color-component. What nearly all cameras do is create a JPEG preview for the RAW file and compute the histogram based on that preview. This shows the correct histogram for JPEG images. If you shoot RAW+JPEG, it is also correct for the JPEG one. For those who shoot exclusively RAW, then obviously the histogram ends up being incorrect.

The discrepancy has to do with how the JPEG preview is rendered which is affected by image parameters. The lower the contrast, the more dynamic-range gets preserved in the 8-bits of space. In theory, one could show the entire range in a histogram but most cameras do not support contrast that low since compressing a high bit-depth image into 8-bit of space with no clipping would make it look extremely dull.

There is no camera screen that can show even 12 bits, since the horizontal resolution is too low. The histogram is always made of buckets each represent more than one luminance or color value, in the case of RGB histograms. If one were simply to drop the lower bits from RAW data, we could have a perfectly representive 8-bit histogram for a RAW file but only one camera AFAIK does this. The issue is that most cameras drop values at the extremes of the RAW values and map the rest to an 8-bit space which is what happens when producing a JPEG image out of RAW data.