Symptoms

SharePoint K2 Integration says that the K2 Service Account user is not an administrator. Receiving error that "K2 Server administration rights are required." and "The logged on user does not have Administrator rights in K2 Server. Please add this user to the Administrators group in K2 server" even though the user does seem to have this right.
 

Diagnoses

Is the application pool for the Sharepoint web application that is hosting the site running under a Domain service account with "Impersonate" rights in K2?
 

Resolution

After adding the Sharepoint application pool account to the K2 Server rights and giving this account "Impersonate" rights, the various issues seen have been resolved.