This issue manifests when RadGridView loaded some columns first (which are working) and then add more columns. The additional columns cannot paste values in their cells.
To work this around, mark the new columns as auto generated and call one of the internal methods.
newColumn.IsAutoGenerated = true;
this.gridView.Columns.Add(newColumn);
var collectionViewPropInfo = this.gridView.Items.GetType().GetProperty("CollectionView", System.Reflection.BindingFlags.Instance | System.Reflection.BindingFlags.NonPublic);
var qcv = (QueryableCollectionView)collectionViewPropInfo.GetValue(this.gridView.Items);
var methodInfo = qcv.GetType().GetMethod("OnElementTypeChanged", System.Reflection.BindingFlags.Instance | System.Reflection.BindingFlags.NonPublic);
methodInfo.Invoke(qcv, new object[0]);