  In the present study, we continue testing the Primordial Group hypothesis
(Casado 2022), which postulates that only sufficiently young open clusters can
be binary or multiple, and old clusters are essentially single. To this end, we
revisit all the remaining binary cluster candidates in the Galaxy having at
least one cluster older than 100 Myr through Gaia data and careful revision of
the literature. We have found no convincing case for an old binary system among
the 120 pairs/groups revised. Most of the pairs are optical pairs or flyby
encounters. However, we have found three dubious pairs that could falsify the
title hypothesis upon further research. We also have found two possible
primordial pairs older than expected. Our results confirm that the vast
majority of binary/multiple OCs in the Galaxy, if not all, are of primordial
origin and are not stable for a long time. This finding is in line with similar
studies of the Magellanic Clouds and theoretical N-body simulations in the
Galaxy. The pairs of OCs in these groups are generally not binary systems since
they are not gravitationally bound. We also point out some inconsistencies in
previous works and databases, such as false open clusters and duplicities.
