The same was said about the Polish AF chequer. If you have a look at the Polish planes used in 1939 you may noticed the nonsymmetric applying of the Polish national marking almost on all Polish aircraft.
Regarding the soviet red star ... I believe it was because of the getting of a kind of a compromise between the year seasons and the colours used for the camo.The red star appeared to be well noticed on the solid green background or the green/black painted surfaces. What is more while the winter camo was in use the red markings were seen greatly. The tone of the red colour should be taken into consideration as well. Contrary to the colour tones used by the Western countries the Russian one was guite bright and gloss mostly. So no wonder the VVS decided to remove them from top surfaces.
Here a couple od shots showing the tops of wings with the red star and without. Although the shots aren't of the greatest qualirty, please notice how nice these are seen if applied.
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the source: the net.