The ammo was a major source of inaccuracy in these. Apparently in the 1990's the Russians had issued some "Dragunov only" ammo for snipers, it was a different projectile and weight, more atuned to stability at long ranges, and apparently sub-MOA.
BUT...the gun has to be in good shape. AND a perfectly zeroed rifle. AND a truly skilled shooter who's putting his skills into it.
All that said, movies and TV are a horrible place to get an impression of weapons performance in the real world. From the 1950's to the 1970's, most actors in Hollywood were WW2 veterans. Today, you basically find no more than about 5 people who were former soldiers...in the entire industry, much less as stars or actors. From the writers, the directors, the actors and the stars...none have worn uniforms, do not know what it's like, have no clue about how weapons work or what they can and can't do.
When they want to "get it right", they hire outsiders who know. And then they proceed to ignore those outsider "technical advisors" if it interferes with the storytelling, or their "vision". Meaning what? Headshots at 850m...do you think that's realistic in real world conditions with ANY rifle, on the battlefield, much less a Dragunov?!? I think that's unrealistic with a top flight rifle/system/combo. Unrealistic for 3/3 targets, without a top rifle, top ammo, top scope, top shooter, and especially without a VERY skilled spotter. IMO.
Actually, ask this question in the Precision forum here, minus the "Dragunov" bit, just ask them how likely headshots are at that distance with a true precision rifle.