  We study the role of systematic effects in observational studies of the
cusp-core problem under the minimum disc approximation using a suite of
high-resolution (25-pc softening length) hydrodynamical simulations of dwarf
galaxies. We mimic realistic kinematic observations and fit the mock rotation
curves with two analytic models commonly used to differentiate cores from cusps
in the dark matter distribution. We find that the cored pseudo-isothermal
sphere (ISO) model is strongly favoured by the reduced $\chi^2_\nu$ of the fits
in spite of the fact that our simulations contain cuspy Navarro-Frenk-White
profiles (NFW). We show that even idealized measurements of the gas circular
motions can lead to the incorrect answer if velocity underestimates induced by
pressure support, with a typical size of order $\sim$5 km s$^{-1}$ in the
central kiloparsec, are neglected. Increasing the spatial resolution of the
mock observations leads to more misleading results because the inner region,
where the effect of pressure support is most significant, is better sampled.
Fits to observations with a spatial resolution of 100 pc (2 arcsec at 10 Mpc)
favour the ISO model in 78-90 per cent of the cases, while at 800-pc
resolution, 40-78 per cent of the galaxies indicate the fictitious presence of
a dark matter core. The coefficients of our best-fit models agree well with
those reported in observational studies; therefore, we conclude that NFW haloes
can not be ruled out reliably from this type of analysis.
