I don't think of it as over-lighting in order to give the colorist the enough material to create the effect, generally the light levels and balance in the original should be close to the effect.
But it does show you that the same lighting if brightened by a mis-exposed camera shooting behind-the-scenes footage can make things look over-lit because now the fill light becomes more prominent than intended once the scene is brought down to the desired level. But behind-the-scenes videos often want to show-off everything happening on the set, they aren't interested in creating moody images.
Yes, there are gamma / contrast issues involved too, perhaps the cinematographer is lighting for a higher-contrast look built into the monitor output to reproduce what will happen in the final grade, but the behind-the-scenes camera is using a flatter contrast, particularly in the shadows. In order to keep noise down in the shadows, it is not unusual to work around a LUT for the monitor that has fairly strong black levels so that you light the set with this in mind, with the idea to apply the same slightly crushed shadow timing in the final grade, so in a sense, you are lighting for the grade so to speak, but not in some sort of open-ended manner of giving a colorist a ton of information and letting them create a look from it after-the-fact. It's more akin to lighting film negative for being printed on a higher-contrast print stock, you are compensating for some loss of shadow detail that the higher-contrast print stock will be giving you.