John Browning, who produced most of the "modern" gun mechanisms, died in 1926, about the time that electric motors were becoming commonplace in factories.
Today there are folks making very functional guns with hand tools in very primitive conditions.
An AK47, on the other hand, well the whole design is based around very loose tolerances for ease of manufacture and for reliability - not as affected by dirt, mud, sand, etc as other designs.
You do for some types of shooting, but in general no.
And, even if you did, what makes you think that 0.01mm requires modern equipment?
Moreover, tight assembled tolerances don't require tight part manufacturing accuracy. You can hand-fit parts.
http://www.armscollectors.com/darra/darra.htm
and a more recent one: