When one person in a group is rude or treated rudely, as in the examples above, it does affect everyone who was there to experience or hear about the rudeness. As much as humans want to think that things just roll off of them and they are okay, subtle feelings of fear and anxiety tend to show up. These feelings cause caution and often times errors in one’s work. In my own observance of rudeness I see how others become fearfull and worried. Instead of feeling confident and valued, they feel worried they will be next to receive criticism. The more worried they become, the more mistakes they make. There is also a lot of chatter about the rudeness and what it means. This chatter disrupts the work flow and less gets done.

That might be a reason that because the person in group 1 was insulted and dismissed; the productivity went low, but that cannot be the only reason for the group 1 being non-productive.
Obviously rude behavior harms but cannot affect to the productivity (that too when it was mentioned with an example above) of the whole team when the team members are from different group.
Being within the team is necessary rather than commanding the team; if you are in team you get more opportunities to understand about the team views and opinions.