Do video formats support colour profiles? Recently, I was reading a wiki, dedicated to one popular cartoon show and stumbled upon an interesting problem: 

From left to right: frames from the US iTunes, Australian iTunes and US iTunes version with CC in a video player 

As you may see, it's the same frame, but colours are different. So, it makes me wonder: does H.264 standard / MP4 container supports any kind of colour profiles (like, ICC in JPEG) and if yes, does any player support it? And what about DVD/Blu-Ray disks? Or there is no way to watch the same version of any video, as it was shot by it's creators? Thanks. :)
No most video formats (nearly all) do not allow custom ICC color profiles to be embedded. (Improvemet/correction: MP4s can have color profiles tagged in the metadata of a video file.) most video on the consumer end is intended for the REC.709 color space. sRGB is similar and uses the same primaries. transcoding (including compressing) will almost always result is a slight shift in color accuracy, saturation, gamma curve, or black and white level shift. This is made worse due to converting between RGB and YCbCr color spaces.