  We present additional HARPS radial velocity observations of the highly
eccentric ($e \sim 0.6$) binary system DMPP-3AB, which comprises a K0V primary
and a low-mass companion at the hydrogen burning limit. The binary has a $507$
d orbital period and a $1.2$ au semi-major axis. The primary component harbours
a known $2.2$ M$_{\oplus}$ planet, DMPP-3A b, with a $6.67$ day orbit. New
HARPS measurements constrain periastron passage for the binary orbit and add
further integrity to previously derived solutions for both companion and planet
orbits. Gaia astrometry independently confirms the binary orbit, and
establishes the inclination of the binary is $63.89 \pm 0.78 ^{\circ}$. We
performed dynamical simulations which establish that the previously identified
$\sim800$ d RV signal cannot be attributed to an orbiting body. The additional
observations, a deviation from strict periodicity, and our new analyses of
activity indicators suggest the $\sim800$ d signal is caused by stellar
activity. We conclude that there may be long period planet 'detections' in
other systems which are similar misinterpreted stellar activity artefacts.
Without the unusual eccentric binary companion to the planet-hosting star we
could have accepted the $\sim800$ d signal as a probable planet. Further
monitoring of DMPP-3 will reveal which signatures can be used to most
efficiently identify these imposters. We also report a threshold detection (0.2
per cent FAP) of a $\sim2.26$ d periodicity in the RVs, potentially attributed
to an Earth-mass S-type planet interior to DMPP-3A b.
