When you get right down to it, the only element of a Sniper Rifle that SR Sniper Rifles really keep is (assuming of course) the better barrels. Most of what makes the rifle a sniper rifle is in the sights attached, and the caliber being used. Most SR Sniper Rifles do not come with scopes of any kind. Many "sniper rifles" are switched from a sniper role to a designated marksman role simply by changing the optics on them (glances at the Dragunov). Yes, some of them are effectively a hunting rifle with a scope. That's where the entire class of weapons came from, even using common hunting rifle rounds. Where a lot of people come into confusion is at the difference between a sniper rifle and a sniper system. Sniper system are merely the rifle with all the added accessories. The M-24 sniper system is a fine example of this. The system includes the rifle and all the accessories that were fielded with it. Of course, now the military is completely refitting the weapon to the point where it isn't even really the same.
You can say they are a precision weapon, but the rules simply do not reflect any advantage for an advanced degree of precision. More to the point, how well balanced and precise any given "sniper rifle" is, varies greatly from rifle to rifle. When you get right down to it, the general standard for precision is usually higher in competition grade rifles than sniper rifles, but again it all comes down to the sights being used.
Attached to an underbarrel mount, they'd still take the edge test as a penalty in any situation not involving being staked up, so not using them correctly does impose a certain impact still.