  We study the role of the lattice artifacts associated with the Coulomb
binding effects in the analysis of the heavy quarkonium within lattice NRQCD.
We find that a "naive" perturbative matching generates spurious linear Coulomb
artifacts, which result in a large systematic error in the lattice predictions
for the heavy quarkonium spectrum. This effect is responsible, in particular,
for the discrepancy between the recent determinations of the bottomonium
hyperfine splitting in the radiatively improved lattice NRQCD [1, 2]. We show
that the correct matching procedure which provides full control over
discretization errors is based on the asymptotic expansion of the lattice
theory about the continuum limit, which gives
$M_{\Upsilon(1S)}-M_{\eta_b(1S)}=52.9\pm 5.5~{\rm MeV}$ [1].
