At the USB-IF compliance workshops, the measurements are always done at the test fixture, never at the chip. The problem may be the termination of the cable. The shield and ground wires should be properly connected to the board. Make sure that the engineering unit and the flexing of the cable hasn't caused the cable to break many of the shield strands. If this occurs, the resistance of the cable will be high.
Also ensure that the USB 2.0 cables/connectors are certified compliant. The USB-IF website (www.usb.org) has a list of certified compliant cables and connectors.
You may also want to check at the chip and see if the offset is lower. Then try a short on the shield to ground to see if the offset changes. Some designs implement a resistor/capacitor network between the shield and the ground to help with ESD and EMI in noisy environments. However, several designs have had the ground and shield shorted without any problems.
If the short on the shield to ground reduces the offset, most likely you have a current flow (small amount), which is giving the offset. The system you are using should have one point where they are connected together. A normal system design would have a single point which connects these two points and the host computer should have this setup.