The content in the OP doesn't really match the Thread title.
Yes, it is true the action of the rifle does affect the accuracy, or rather precision, of the rifle. No, this pseudoscience of action "air tightness" isn't a factor. As
@Bushpilot mentioned, the brass is the effective seal for the system. Consistency and symmetry of lockup is what matters. A bolt action rifle will typically have a more symmetric lock up - long term - than a break barrel.
"Distance," or effective range, is a factor of retained velocity at range. Retained velocity at range depends upon initial velocity, Muzzle velocity, as well as bullet aerodynamics, ballistic coefficient, and upon environmental conditions, density altitude. None of that really affects PRECISION, really, but it is easier to shoot long distance with a flatter shooting bullet and cartridge.
Semi-automatic, centerfire rifles are typically NOT sealed bore, so they lose some muzzle velocity compared to a sealed bore action with the same barrel length, like a bolt action or break action. Semiautos use some of the expanding gases to operate the action. The action lock up design and reciprocating mass also tends to rob semiauto rifles of some precision. They trade a bit of precision for an increased rate of fire. But for most practical pursuits - that is hunting or soldiering - the target size is sufficiently large such the difference in impact velocity really doesn't change the effective range terribly.