A good Bolt-action rifle is still superior to semi-autos rifles for accuracy. If all I wanted was precision, long range accuracy, I wouldn't even consider a semi-auto.
As already stated - not true. The real difference is that you'll be in the $3K range for an AR style .308 that will do >.5 MOA at 100 yards. You can probably get that out of a $1500 bolt gun with a little work on it.
There are a couple of other things with an auto versus bolt gun. If you reload, you'll have to full length resize the cases to get them to feed properly in an auto. With a bolt gun, if you're very careful on overall cartridge length (case stretch at the neck), you can neck resize only for 3-4 uses. By doing that, you're using fire-formed cases and you're accuracy will improve very slightly because the case is fitted to the chamber.
Lastly is weight - if that is a concern. I have an AR 308 with a 20-inch barrel, and with the scope on it, it's about 14 lbs. A bolt gun, with a medium weight barrel, should be in the 11 lb range with a scope.