IME, there's a world of difference between any FMJBT and the HPBT match bullets cited by dleong. Decent M193-type bullets will almost always do 3 MOA, and you might find loads to do 2 MOA (I have found several that did so out of 1-12 and 1-9 barrels), and some people report close to 1 MOA with really good lots of FMJBTs and a few legendary lots of surplus M193-type ammo...but only if fired from match barrels. I suspect many of these performances are with 3-shot groups, which reveal amost nothing from a statistical repeatability standpoint, especially if you're shooting 10-shot strings on a typical HP match.
Your HPBTs from Sierra, Hornady, and Nosler should all shoot 1 MOA or less all day long from any decent barrel and every "match" barrel. If not, something's wrong or your got a bad barrel. A good barrel will do 1/2 MOA if you do your part--I've seen others do it with iron sights, too.