I’ve heard this all my life—that bolt action was more accurate than semi-auto—but no one can really explain to me why. Is it just a “thing” people just parrot—because that’s what they’ve always heard too—without any proof?As I've always understood it, a semi-auto has more moving parts. Each of these parts moves in multiple directions, some directions are primary movement while some are just due to mechanical tolerances. With each moving part comes variability and variability is the enemy of accuracy.
The end effect of all this variability is that each round tends to seat ever so slightly differently from the previous round. Head spacing will be slightly different. Gas pressures will be slightly different which results in slightly different functioning of the action. When fired, the firing pin doesn't strike the primer dead on either.
These points of variability and others tend to adversely effect the accuracy of a semi-auto more than that of a simpler bolt action rifle.
A few years back there was an improved bolt action that uses electrical current to light the powder. The result was better accuracy because you don't have the mass of the moving hammer and spring imparting motion to the carefully aimed firearm. The "lock time" is the time from when the sear releases the hammer and the firing pin strikes the hammer. The electric version has essentially zero "lock time". The longer the lock time, the more likely that the mechanical motions in the action will move the intended aim point. When you move to a gas operated mechanism, there is usually a large piston set in motion as the bullet passes the gas port. That introduces even more mechanical motion beyond that introduced during the "lock time" of the action.
You can read about the Remington 2000 ETronX rifle where the timing issues are discussed in detail.