I must say that I read these kinds of threads with a bit of detached amusement.
$4,000? You're kidding, right? It never ceases to amaze me how so many people think that the more money you spend, the better a rifle or shooter you will get.
To provide you with a bit of a counter-example, here is an admittedly provocative thread I posted last spring:
http://www.canadiangunnutz.com/forum/showthread.php?t=218941
It is a story about a rifle that is cheaper than pretty well ANYTHING that ANY F-class shooter has ever used in competition. I mean, the whole deal is probably worth less than $750, and that INCLUDES the Leupold 6.5-20 scope! Actually, the $750 is somewhat arbitrary because I could probably get that much for it simply because of its proven performance. It's not a reflection of the actual value of the parts.
If you read that thread, you'll learn that this rifle shoots into the .2s after having the barrel so badly rusted that I could not even see daylight through the bore. It's also worth noting that I've taken it to the range several times since I posted that thread last spring. It has consistently shot at this level since then, so the results I posted in that thread are no fluke.
In my opinion, this establishes that any decent, concentric, front-locking bolt action that is properly barrelled and bedded, and scoped with a precision optic, and fed proper handloads made with decent components, chambered for an appropriate cartridge, will be able to shoot less than 1/2 m.o.a. consistently, IF THE SHOOTER IS UP TO THE TASK. Just think about what I have been able to achieve with a crappy, WWI action, cobbled together from mixed parts, thrown into a random wood stock, with a hand-me-down barrel THAT WAS RUSTED ALMOST INTO OBLIVION.
It's not how much you spend on the rifle; it's how much attention you personally pay to the necessary details.
In this regard, I consider myself a disciple of Mysticplayer, who has, time and time again, proven that you can take cheap actions and make accuracy masterpieces out of them, if you pay attention to detail and use your imagination.