We analyse the environmental properties of 370 local early-type galaxies (ETGs) in the MASSIVE and ATLAS^3D^ 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*10^9^<~M*<~2*10^12^M{sun}. 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 Nth 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 ~0.4 to below 0.1 with increasing mass, and the fraction of slow rotators f_slow_ increase from ~10 to 90 per cent. 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_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.