LED restricted minimum current (do not use below 10mA)
A look at this application note may be illuminating. 

Too far from the grouping current the variation in LED brightnesses is such that an array of them may appear very uneven.



As @Ignacio mentions, it's also possible the color temperature will vary from the ideal at very low currents, although it does not seem to be a very strong effect according to this paper. 



Perhaps the "strictness" of the warning is explained by cultural factors.