This is valid only as long as the victim completely stops the projectile all but instantly
this would be maybe the case of a soldier with substantial body armor that would not shatter, but completely absorb the energy of the impact.
yet modern body armor is made to dissipate as much energy as possible, and not all the momentum of the is transferred directly, as it most unusual to land a hit at such a right angle (in which case, even body armor might fail depending on conditions)
in any case where the projectile does not decelerate almost instantly, the basic equations for energy transfer are largely unfit - without armor, a 7.62 round will almost always result in a fairly gruesome exit wound -- 5.56 often has higher velocity, and with a lesser area it exits the target even more frequently
so not all the energy in the bullet-victim system is transferred kinetically at the point of impact, which is why it is in fact reasonable a person who is not killed could remain standing from a physics standpoint alone
also -- the OP's math did not account for the added weight of gear a soldier would carry... also, in combat it is not wise to stand upright too much, which lowers the torque arm as well...
some modded versions of the M82 .50cal rifle DO actually deliver enough power to lift a target off his feet and land his expired remains several feet behind himself... those are pretty fun to try in the arsenal (and some MP servers DO allow those as well)
also very much noteworthy -- how come doesn't the shooter flip backwards himself according to your logic?
the recoil energy acting on a gun and being absorbed by the shooters arms will almost certainly exceed the total momentum of a projectile onto its target, after having travelled through air friction and leading-shock compression (bullets go supersonic, air will compress before giving way at that speed, hence that "crack" when they go by, a tiny sonic boom)
if the shooter can fire and not topple on his back, the target can conceivably receive the round and remain upright
the M82 mentioned earlier is fitted with a very beefy recoil damper system - it is also not meant for firing whilst standing up (bipod and prone, lest lots of hurt to him behind the buttstock)
and lastly - this can only be verified for certain by way of experiments, of course -- yet I don't think it'll be easy trying to find test subject volunteers