I have noticed that upset toddlers turn their back to someone who wronged them and huff. Most adults don't do this, so I don't know how this could be a learned behaviour. Do other animals express this behaviour? I do not see how this could be specific to culture.
Sulking is the behavior you are refering to and it is seen in orangutan, Chimp and Bonobo. Likely in other primates but I am not aware of any published works. I have heard about it in baboons but have not read the papers myself.
Also adult humans DO do this on occasion, it is just often more subtle.
It is amazing how many identical social behaviors are seen in our close relatives, especially the ones about conflict and conflict resolution.