Smoke, Not true, The gun comes back and the bullet goes forward. That is where the forward energy goes. Crossbows do have forward recoil just like an upper in break barrel air gun.
However, the physics are different. Way more energy goes forward on the crossbow because that is the way the limbs fly upon release. There is so little resistance from a normal arrow that you don't have the back push.
In some testing we did, we shot a solid piece of steel, the same size as an arrow, and it pushes you back as the arrow shoots due to the increased resistance.
They do reinforce crossbow scopes a little diferently then rifle and shotgun scopes. While most upper end ($200) scopes will survive the punishment a crossbow dishes out, the lower end ones often do not. The bad part is, most do not break the crosshairs. Most times the crosshairs start to "float" so you don't know they are broken. You first think the arrow is bent, or you pulled your head, or the broadhead planed, or your sting or cables stretched, or you have a screw loose (and sometimes at this point you do).
Randy