Observations have revealed that disturbances in the cold neutral atomic hydrogen (HI) in galaxies are ubiquitous, but the reasons for these disturbances remain unclear. While some studies suggest that asymmetries in integrated HI spectra (global HI asymmetry) are higher in HI-rich systems, others claim that they are preferentially found in HI-poor galaxies. In this work, we utilise the ALFALFA and xGASS surveys, plus a sample of post-merger galaxies, to clarify the link between global HI asymmetry and the gas properties of galaxies. Focusing on star-forming galaxies in ALFALFA, we find that elevated global HI asymmetry is not associated with a change in the HI content of a galaxy, and that only the galaxies with the highest global HI asymmetry show a small increase in specific star-formation rate (sSFR). However, we show that the lack of a trend with HI content is because ALFALFA misses the gas-poor tail of the star-forming main-sequence. Using xGASS to obtain a sample of star-forming galaxies that is representative in both sSFR and HI content, we find that global HI asymmetric galaxies are typically more gas-poor than symmetric ones at fixed stellar mass, with no change in sSFR. Our results highlight the complexity of the connection between galaxy properties and global HI asymmetry. This is further confirmed by the fact that even post-merger galaxies show both symmetric and asymmetric HI spectra, demonstrating that merger activity does not always lead to an asymmetric global HI spectrum.