The best barrels don't usually group factory ammo under 1/2 MOA for long strings or several groups, but learning how to reload for accuracy; choosing the right bullets, great powder for the cartridge/bullet weight; testing bullet seating depth, various primers, sorting cases by make/times fired, weight, lot numbers and other factors often make the difference between winning or losing matches. The "Nut" behind the buttplate and his/her ability to be very consistent in holding, aiming, squeezing is the last big factor. You can't replace the "Nut", but it can be educated and seasoned.
Weather; especially wind, light, mirage are also important when striving for accuracy. I can't shoot as well at my home range because the mirage and wind are so bad. The Capitol City Multi-Purpose Range in Augusta, ME is about the best place I've encountered for consistency, especially when the sun has moved Southerly in mid-late morning. The ground is mostly "dead" sand so mirage isn't often a big problem.