You guessed it right: it's a problem you can't fix in post, and most of us may never notice it until we get to the color grading phase. If your camera costs less than $10,000, you'd better be aware that it has probably got the blues.
The problem occurs when you shoot in low-light situations, and there are lots of prominent bright blue areas in the frame. The sensors on most consumer and prosumer cameras seem to have a very peculiar sensitivity towards blue in that situation. Is it related to the fact the blue channel has most of the noise in the footage? I don't know. The author of the video doesn't know either, but notes that this occurs when using a non-raw file encoding, such as ProRes, AVCHD, and the like. He demonstrates the problem in the Sony a7S. A possible solution is to change the color temperature until the clipping is gone and then alter the color temperature back in post.
I tested this myself with a sub-$10,000 Canon cinema camera, and indeed, the problem existed in the blue channel. I tried a similar situation with red and orange objects, but they didn't clip as quickly as the blue channel did. Changing the color temperature seems to really prevent the problem from happening.
Have you tried this on more expensive cinema cameras? Please, tell us in the comments.