How bright are the outer planets, when at close range?
There is a rule about average surface brightness: it is conserved as you change distance or magnification.  For the gory details see.  Telescopes make unresolved objects brighter, but for resolved objects, a telescope shows you the actual surface brightness (assuming that the exit pupil diameter is well matched to your eye's pupil (~7mm) and is not throwing away light, dimming the view).   The surface brightness of any resolved object through a telescope is the same as it would be if you were there.
Also, the 0.01 of earth sunlight received at Saturn is way more than the lighting provided by a full moon which is 400,000 times fainter than the Sun.
What you also need to take into account, is that when you look at Saturn through a telescope, it is generally (not always) done at night when your eyes are dark adapted.