Your bar is set too low
I used to shoot a Russian SKS back in the 90s out to 200 with irons, reliably hitting a 4" gong. They're not tack drivers - they weren't ever made to fill that expectation - but those suckers are far more accurate than most give them credit for, and enough to 'get the job done' at a decent range. 75-100? Easy!
As for the general action comparison, I think it's hard to do that without understanding more about the requirements of the task at hand. I shoot a semi-auto at 200, 300 and 600 yards and know that if I do my job, it does its job really well. However, semi-autos usually need sloppier tolerances to accommodate a violent and imprecise action, along with an expectation of dirt, oil, and other rough operating conditions. The best bolt-action, made for the pristine bench environment with classical music playing in the background, is going to outperform a semi-auto in a pure tack-driving exercise all day long.
So, I think your grandpa's right, in a vacuum. The rifle itself may be more accurate, but perhaps not as "effective" in different conditions as a semi-auto or lever action.