
Yup, after doing some googling and youtubing on my own regarding GY6 starters, either it wasn't the starter or you got lucky and the flywheel slung the lube to the right spot.
Check out this GY6 cutaway from
http://www.chinesescooterreference.com/manuals_charts.htm (great site for GY6 info, btw) and you'll see that instead of a "regular" starter with a gear that engages / disengages the flywheel, the GY6 starter drives a reduction gear that drives that drives a "starter clutch" that grabs the crankshaft directly, all this gearing is located inside the crankcase behind the stator, behind the flywheel.
My money is that it's either not the starter at all, or it's something else behind the flywheel, or it IS the starter and for some reason it has decided to be quiet on its own. Either way, I think I'd take the flywheel cover off and take a good look for anything amiss.