Well, on the surface level, Team B lost their first match and won their second, while team C won their first match but lost their second, so clearly order matters.

On the more meta level, a format optimised for selecting one winner has been poorly adapted to the task of selecting three winners and ranking them. Adjusting the format to fairly select silver and bronze would add complexity and cost and time, and apparently not enough people care enough about fairly selecting silver and bronze for this to have happened.