  We analyse the environmental properties of 370 local early-type galaxies
(ETGs) in the MASSIVE and ATLAS3D surveys, two complementary volume-limited
integral-field spectroscopic (IFS) galaxy surveys spanning absolute $K$-band
magnitude $-21.5 > M_K > -26.6$, or stellar mass $8 \times 10^{9} < M_* < 2
\times 10^{12} M_\odot$. We find these galaxies to reside in a diverse range of
environments measured by four methods: group membership (whether a galaxy is a
brightest group/cluster galaxy, satellite, or isolated), halo mass, large-scale
mass density (measured over a few Mpc), and local mass density (measured within
the $N$th neighbour). The spatially resolved IFS stellar kinematics provide
robust measurements of the spin parameter $\lambda_e$ and enable us to examine
the relationship among $\lambda_e$, $M_*$, and galaxy environment. We find a
strong correlation between $\lambda_e$ and $M_*$, where the average $\lambda_e$
decreases from $\sim 0.4$ to below 0.1 with increasing mass, and the fraction
of slow rotators $f_{\rm slow}$ increases from $\sim 10$% to 90%. We show for
the first time that at fixed $M_*$, there are almost no trends between galaxy
spin and environment; the apparent kinematic morphology-density relation for
ETGs is therefore primarily driven by $M_*$ and is accounted for by the joint
correlations between $M_*$ and spin, and between $M_*$ and environment. A
possible exception is that the increased $f_{\rm slow}$ at high local density
is slightly more than expected based only on these joint correlations. Our
results suggest that the physical processes responsible for building up the
present-day stellar masses of massive galaxies are also very efficient at
reducing their spin, in any environment.
