I have two Stevens 200 and they both shoot great when shot properly and not put undue force at the fore end tip. If you are using a sling tightly I could possibly see problems by letting the stock touch the barrel. I would be more inclined to blame bedding screw torque or the load itself for group size. (barrel vibrations)
Yes the fore stock will move but keeping your bags or rest away from the fore end tip of the stock should be all that is required to eliminate stock and barrel flexing.
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