ArcMap is telling our users that data from a certain feature dataset needs to be registered as versioned to edit. ArcCatalog is showing us that the feature dataset in the SDE is not registered as versioned. My question : How does ArcGIS know that the data should be versioned?
ArcGIS is set up to edit only versioned data in ArcSDE by default. You can change this behavior in if you need to edit SDE data that is unversioned.
See the documentation for v10.0 at Configuring an ArcMap edit session to perform nonversioned edits