In this test, when shooting log at 20,000 ISO the C300 seems to have the same sensitivity as the other camera at more standard picture profiles set at 6,400 ISO.

F3 - C300 - 1D side by side on Vimeo

That the camera is less sensitive when using a log curve doesn't surprise me, but the impression is the C300 doesn't adjust its ISO display to reflect the lower rating.

Of course, the on screen data could be incorrect.

Yes, that is confusing.

Historically Canon has been careful with their ISO ratings. I expect that the rating is technically accurate, but complicated as the compression of dynamic range isn't linear. Perhaps the actual ISO spec isn't as simple as exposing mid grey.