Let me see if I have this right.
If I create a new group with "update capabiltiies" I won't be able to see it in the "Share" list and since no one can see it, no one can add content to the group.
Once a group has been created you cannot turn off this "update" flag because that is forbidden. I have to delete the group and create it again making sure I don't check the last option, which is not called "update capabilities" on that page; it's under "What items in the group can its members update? " and the option "All items (group membership is limited to the organization" which sounds exactly like what a group is for versus "Only their own items" which does not sound like group write permissions so it's only natural (and wrong) to select the "All" option.
It's not much of a hardship to delete and recreate the group because it won't have any content in it and is basically useless until you do so.
So, I can see how it would be hard to document this. Knowing now that the option is useless I will no longer try to use it. This is in that "no on this is a feature not a bug" category, right?