Unable to update features in tables without FID: How to use gid field as the FID column with ogr/gdal python?

I'm trying to update a PostGIS table using the SetField() method in python. The table is imported from a shapefile with pgsql2shp so it has a gid field, which can be used as FID or primary key.

However, when executing SetField(), I get an error saying:

Error 1: Unable to update features in tables without a recognised FID column. 

I tried different things. The only thing that allows updating is to externally add and populate a new column called ogc_fid. Even adding a 'fid' column won't do.

Is there a way to tell ogr/gdal (as of gdal2.1.3) in the python code itself that an existing field such as gid is the FID column?