Debris discs are typically revealed through the presence of excess emission at infrared wavelengths. Most discs exhibit excess at mid- and far-infrared wavelengths, analogous to the solar system's Asteroid and Edgeworth-Kuiper belts. Recently, stars with strong (∼1%) excess at near-infrared wavelengths were identified through interferometric measurements. Using the HIgh Precision Polarimetric Instrument, we examined a sub-sample of these hot dust stars (and appropriate controls) at parts-per-million sensitivity in SDSS g′ (green) and r′ (red) filters for evidence of scattered light. No detection of strongly polarized emission from the hot dust stars is seen. We, therefore, rule out scattered light from a normal debris disk as the origin of this emission. A wavelength-dependent contribution from multiple dust components for hot dust stars is inferred from the dispersion (the difference in polarization angle in red and green) of southern stars. Contributions of 17 ppm (green) and 30 ppm (red) are calculated, with strict 3-σ upper limits of 76 and 68 ppm, respectively. This suggests weak hot dust excesses consistent with thermal emission, although we cannot rule out contrived scenarios, e.g., dust in a spherical shell or face-on discs. We also report on the nature of the local interstellar medium (ISM), obtained as a byproduct of the control measurements. Highlights include the first measurements of the polarimetric color of the local ISM and the discovery of a southern sky region with a polarization per distance thrice the previous maximum. The data suggest that λ max, the wavelength of maximum polarization, is bluer than typical.