I am using the only connection that lets me do schema changes. So it is MY highest level of access. The point of the question was that I can remove any other field I want to except this field.
According to ArcCatalog, SDE is the owner of the table (it was set up that way years ago, so I can't explain why, except that it is behind an extreme level of firewall protection.) As far as not using SDE user, we were forced suddenly into Operating System Authentication, but it did not work correctly for schema changes and perhaps has other issues, otherwise, I would have been able to stop using database authentication. I am the DBA for GIS, but not the SQL Server admin.