A couple of things:
First, MOA is a measure of precision, not accuracy. You can have a gun that shoots 1 MOA and still miss the target. Fortunately, a precise gun can be made accurate by adjusting the sights until they are on target. An accurate gun - one where the center of the spread is right at the point of aim - cannot necessarily be made more precise.
Second, ammo play a huge factor in precision. You'll find that real sub MOA rifles deliver that kind of accuracy using a particular load. Be skeptical of anyone who claims their rifle is sub MOA without specifying a particular loading. The variation in almost all military ammo (excepting specific match ammunition) ensures that no one is going to shoot sub MOA groups with surplus ammunition no matter what the rifle is. A great rifle cannot compensate for ammunition that is only capable of three or four or six MOA.
One thing I have discovered about AKs is a lot of their reputation for being wildly inaccurate comes from shooting military surplus ammuntion. Shooting good commercial or handloaded ammunition from an AK can be an eye opening experience.
Finally, the AK is what it is. Keeping in mind that 70% of all infantry small arms fire occurs at 100 yards or less, and 90 at 300 yards or less, the AK has enough accuracy for its envisioned role as a superior SMG. 4 MOA is adequate to strike a human torso at 300 yards. More than adequate for ranges like 75 yards (the average range of engagement in the ETO during WWII).
Like any tool, you should employ the AK withing it designed parameters. You wouldn't drive a screw in with a hammer (well, some might).
The AK was not meant to be a precision rifle or a hunting rifle. It was designed to be a combat rifle for use at normal combat ranges in a very hostile environment. It is designed to go bang every time and hit someone less than 100 meters away, despite abuse and neglect, in any weather.