I don't know what that guy is talking about shadowcat. We don't have to take his word on it. If a bullet can only move something the same weight as it then how come I've sent heavy steel panels cart wheeling around in the dirt from a small 9mm round. If a person is strapped to something they won't move. If you hit dead center mass they might not move much from a high velocity round. But hit someone with a glancing blow with a hollow point and it'll spin them around a little.
His description of why was a little off, but the fact is, he was a soldier for 20 years and saw it on the battlefield. You can make all the scientific explanations you want, but they only have meaning if they match real world observations.
Nail's statement was "A bullet can only move something around it's own weight." is somewhat true, but its more of a tendency. Think of a newton's cradle, you pull two weights back, and when they strike, two weights are pushed off on the opposite side. This is only true when there is something of equal weight that can accept the force though. When you shoot a metal target, the bullet is stopped, but the energy has to go somewhere. Some of the energy is put into deforming the bullet, some is turned into heat from pressure and friction, and the rest goes into pushing the target back.
A more accurate description is that the bullet cant push more on the target than the recoil puts on the shooter, but that's just in a perfect world, in the real world, the actual force on the target is much smaller than recoil, which isn't a very big push in the first place for most firearms.
But soft targets aren't as good at transferring energy, you still have the energy loss from deforming the bullet as well as heat, but a lot of the energy is put into tearing a hole. Think of preparing meat with a knife, you need to put a decent amount of force to make each cut, and that's with a razor sharp blade. The target has to provide an equal amount of resistance to tear the hole, but most of that is provided by momentum, even stationary momentum is enough. If the target moves after being shot, it is a reaction to pain, or involuntary muscle contractions, but these are lessened by adrenaline while on a battlefield.
But anyway, all of this was mostly for jessalon who seems interested in the physics behind it. When it comes down to it we have an experienced soldier who says that people do not visibly recoil when shot, at least not from the force of the bullets.
P.S. Jessalon, you mentioned that HP ammo is able to transfer more energy to the target, due to the bullet flattening out, creating more blunt force. That is true, but military organizations do not use HP ammo, as bullets designed to flatten or fragment were considered inhumane at the Hague Conventions.