The Support Request that I submitted about it: Support Request #61722
At the end of the FAQ, it's mentioned that there's a security risk with renaming a group. Well, there's a security (or just plain weird) risk with totally remaking groups as well. If you delete a group and then make it again with the same name, any posts to the original group will no longer have the correct security level. They will be set to Groups, but to no specific group, and therefore essentially private. I guess it's not a security risk, but it's something that I'm sure other users have done and assumed would work (I did). For example, let's say I have Group1, and made a post to Group1. And then later on I delete Group1, and remake it with the same name. Most people would assume that that past entry would still allow those people in Group1 to read the entry. However, this is not the case, as the names have nothing to do with how groups are referenced (they use numbers instead). The past post is now essentially private, and no one will really know about it unless they happen to check.
Hm, I can't really think of a good way to word that for the FAQ, but if someone's willing to do it, that'd be great. Feel free to use parts of what I said if you feel like it.
I hope this made some sense. :)