Yeah, if I had to guess what happened, it's something like this.
Cook went to take a leak so he ends up walking out late and surrounded by City team. They start trading some light bants, Pep being Pep has different concept of personal space than a 50 year old, proper hard Brexit Englishman like Cook. Cook understandably feels a little threatened and out-manned, so he overreacts, then everybody else overreacts and suddenly it's all handbags out.
It doesn't look pretty but I'd bet my money that the whole thing would already blow over if media weren't trying to milk it.