Thank you for your replies, Alfred.
Unfortunately this error appears quite randomly.
I just did the same operation again and instead of displacing the object 0.01 units ACAD decided to displace 0.001 units:
Command: CP COPY 46 found
Current settings: Copy mode = Single
Specify base point or [Displacement/mOde/Multiple] <Displacement>:
Specify second point or [Array] <use first point as displacement>:
Command: *Cancel*
Command: Specify opposite corner or [Fence/WPolygon/CPolygon]:
Command: CP COPY 2 found
Current settings: Copy mode = Single
Specify base point or [Displacement/mOde/Multiple] <Displacement>:
Specify second point or [Array] <use first point as displacement>: _from Base point: <Offset>: .01
Command: DI DIST
Specify first point:
Specify second point or [Multiple points]:
Distance = 0.001, Angle in XY Plane = 180, Angle from XY Plane = 0
Delta X = -0.001, Delta Y = 0.000, Delta Z = 0.000
Command: DIST
Specify first point:
Specify second point or [Multiple points]:
Distance = 0.001, Angle in XY Plane = 180, Angle from XY Plane = 0
Delta X = -0.001, Delta Y = 0.000, Delta Z = 0.000
Command: Specify opposite corner or [Fence/WPolygon/CPolygon]:
I mesured the displacement afterwards...
It looks to me like autocad decides to round off numbers at random in this operation. Sometimes it jumps to 0.02 instead of 0.015 and similar. Since this is a very frequent tool in my drafting it is unfortunate to not be able to trust ACAD on moving the object to an exact number.