Social network marketing channel is apparently set up correctly, but it isn't collecting any data. If it was set up correctly, it would be collecting data.
The only exception to that is that there aren't any social media referral traffic, however, it is being insisted that there is indeed social media referral traffic coming in.
Something isn't working correctly, but at this point it is literally impossible to troubleshoot without gaining access to your report suite. I would recommend reaching out to customer care so they can directly access your report suite and marketing channel processing rules to determine exactly what the culprit is.
The segment creation tool only looks at the last 90 days as well, so if you haven't gotten any social media traffic in that time, it won't show in the dropdown. You can still manually enter it, though - just make sure it's exact or else it won't pull data.
It looks like you're already set up perfectly to do this. In the report that you already have pulled up, break down "Social Networks" by the "Last Touch Channel Detail" dimension. You're setting that to store the referring domain of each visit labeled as a Social Network, and the Channel Detail report will have the exact same attribution settings as your Channel report.