QSqlTableModel::headerData() provides column numbers when row 0 is an inserted row (not in the query)

The strings come back in play after full update via select(). As far as I can see from the sources, this might be when QSqlTreeModel::headerData() falls down to default implementation of QAbstractItemModel::headerData(). This seems to be the true case for the just inserted columns. See QSqlQueryData::headerData().

This issue arises even when the set of columns remains unchanged.