SuWt 2 is a planetary nebula consisting of a bright ring-like waist from which protrude faint extended lobes - a morphology believed to be typical of progenitors which have experienced a close-binary evolution. Previous observations of NSV 19992, the star at the projected centre of SuWt 2, have found it to comprise two A-type stars in a 4.9 d eclipsing orbit, neither of which could be the nebular progenitor. Radial velocity studies provided a hint that the systemic velocity of this double A-type binary might be varying over time, suggesting the presence of a third component hypothesized to be the nebular progenitor. Here, we present an extensive radial velocity monitoring study of NSV 19992, performed with the high-resolution Ultraviolet and Visual Echelle Spectrograph mounted on the European Southern Observatory's Very Large Telescope, in order to constrain the possible variation in the systemic velocity of the A-type binary and its relation to the progenitor of SuWt 2. The observations, acquired over a period of approximately one year, show no evidence of variability in the systemic velocity of NSV 19992. Combining these new observations with previous high-resolution spectroscopy demonstrates that the systemic velocity is also stable over much longer periods and, moreover, is distinct from that of SuWt 2, strongly indicating that the two are not associated. We conclude that NSV 19992 is merely a field star system, by chance lying in the same line of sight as the nebular centre, and that it bears no relation to SuWt 2 or its, as yet unidentified, central star(s).