A note about NTFS permissions when used with Sharing permissions:
When using share permissions and NTFS permissions together, if there is a conflict in the configuration, the most restrictive permission prevails
http://www.ntfs.com/ntfs-permissions-combined.htm
That means if your red X'ed administrators, or no a missing homegroup is trying to access a shared permissions file the NTFS permissions will deny it if it is included in the last picture on the right. Appearing to have share access, but then will be denied. I believe this is what is happening. It is hard to tell with all the redaction. Your screen shots are only showing permissions for one account at a time, and to assume they are the same across all accounts would be stupid on my part. You may need to add Everyone or Homegroup to that final folder on the right in the picture, or you may just need to correct an NTFS permission on an existing account.