By itself, a 1/16th of an inch offset would not cause the score or crossbow to shoot poor groups.
It could potentially cause you to not be able to zero the scope because you run out of windage-control (left/right) travel, or could even cause you to damage your scope if you keep cranking on the windage knob until something breaks.
I still suspect something is loose. Poor groups are almost always due to something being loose, or more generally that something is inconsistent from shot to shot.
A fixed bias offset can make set-up difficult or impossible and would cause your bow to not shoot to a point of aim of your choosing. It would not cause arrows to scatter.