How many groups can possibly be made every week? I don't see how introducing some delay where every few days/every week someone comes along and approves each new batch of groups would be too much extra workload for the moderators they already employ.
And the fact is, by having these social features both Xbox, Playstation and Steam have created their own social networks, so they should have the same social responsibility that any other social network should have. If they're not able to moderate these features properly they shouldn't exist to begin with.
But they are, that is why the report functionality exists. As much as I'm on board to accept this is offensive and unacceptable on XBL, I'm not quite signed up to anyone in here acting like their day is ruined and they can't turn on their Xbox again without fearing the dashboard. Like with a lot of content creation on networks, things will slip through automatic detection, or simply need to be reported. That's why decent reporting tools are required. All of this content, whether it be groups, usernames, messages or more can be traced back to account creators, and as it says in the T&C for these services your account can be terminated or suspended as a disciplinary action. MS will already be inundated with constant reports of rude messages on XBL and soundclips of recordings from screaming teenagers playing Halo. You'll find the teams that moderate the online network handle a whole host of reports.
If MS do not do anything about this being reported, then you can be more on their case. For now it's just one example of something that may slip through a word blacklist, as it doesn't expclicitly state "Nazi", and image detection, as the swastika, while incredibly recognisable despite some trolling this topic saying "it's not a swastika", is a shape, so, AI shape detection always has to air on the side of caution. It's not quite the same as nudity filters which have a much higher hit ratio of not producing false positives. This is why games like LBP even panic about allowing users to upload their own images, as it's a nightmare to try and moderate. As I said automatic nudity detection is usually much more effecient than trying to automatically shoot down shapes.