That's incorrect. Anything released from earth carries the same inertial momentum. It's like when you throw a ball in a running car.
For objects above the earth's surface, the radius of the 'orbit' around the center of earth increases, and thus the 'forward' component of the velocity has to increase in order to stay over the same point on the earth. If you shoot something high enough straight up, it will land to the West of the point it was launched from. (This does ignore effects of wind and such, but I believe so did your argument).