  Recent numerical work by Wilson, Mathews, and Marronetti [J. R. Wilson, G. J.
Mathews and P. Marronetti, Phys. Rev. D 54, 1317 (1996)] on the coalescence of
massive binary neutron stars shows a striking instability as the stars come
close together: Each star's central density increases by an amount proportional
to 1/(orbital radius). This overwhelms any stabilizing effects of tidal
coupling [which are proportional to 1/(orbital radius)^6] and causes the stars
to collapse before they merge. Since the claimed increase of density scales
with the stars' mass, it should also show up in a perturbation limit where a
point particle of mass $\mu$ orbits a neutron star. We prove analytically that
this does not happen; the neutron star's central density is unaffected by the
companion's presence to linear order in $\mu/R$. We show, further, that the
density increase observed by Wilson et. al. could arise as a consequence of not
faithfully maintaining boundary conditions.
