We discuss strategies to make inferences on the thermal relic abundance of a Weakly Interacting Massive Particle (WIMP) when the same effective dimension-six operator that explains an experimental excess in direct detection is assumed to drive decoupling at freeze-out, and apply them to the explicit scenario of WIMP inelastic up-scattering with spin-dependent couplings to protons (proton-philic Spin-dependent Inelastic Dark Matter, pSIDM), a phenomenological set-up containing two Dark Matter (DM) particles χ 1 and χ 2 with masses m χ =m χ 1 and m χ 2 =m χ + δ that we have shown in a previous paper to explain the DAMA effect in compliance with the constraints from other detectors. We also update experimental constraints on pSIDM, extend the analysis to the most general spin-dependent momentum-dependent interactions allowed by non-relativistic Effective Field Theory (EFT), and consider for the WIMP velocity distribution in our Galaxy f (v) both a halo-independent approach and a standard Maxwellian. Under these conditions we find that the DAMA effect can be explained in terms of the particle χ 1 in compliance with all the other constraints for all the analyzed EFT couplings and also for a Maxwellian f (v). As far as the relic abundance is concerned, we show that the problem of calculating it by using direct detection data to fix the model parameters is affected by a strong sensitivity on f (v) and by the degeneracy between the WIMP local density ρ χ and the WIMP-nucleon scattering cross section, since ρ χ must be rescaled with respect to the observed DM density in the neighborhood of the Sun when the calculated relic density Ω is smaller than the observed one Ω 0 . As a consequence, a DM direct detection experiment is not directly sensitive to the physical cut-off scale of the EFT, but on some dimensional combination that does not depend on the actual value of Ω. However, such degeneracy can be used to develop a consistency test on the possibility that the WIMP is a thermal relic in the first place. When we apply it to the pSIDM scenario we find that only a WIMP with the standard spin-dependent interaction O=χ 1 γ µ γ 5 χ 2q γ µ γ 5 q +h.c. with quarks can be a thermal relic for, approximately, 10 GeV < ∼ m χ < ∼ 16 GeV, 17 keV< ∼ δ < ∼ 28 keV, and a large uncertainty on Ω, 6 × 10 −7 Ω 0 < ∼ Ω < ∼ Ω 0 . In order for the scenario to work the WIMP galactic velocity distribution must depart from a Maxwellian. Moreover, all the χ 2 states must have already decayed today, and this requires some additional mechanism besides that provided by the O operator.