I'm pretty sure those grounds have to be connected..
There is a 12Vdc 'connection' back to the input, but it's possible that
it's on the + side, and it won't make any difference.
It's also possible mine is using an Opto-isolator to couple the PWM back..
That would really be the best way to design these things..
You do
not want one side of the AC line to be felt out on the DC end
of your cell phone charger..
One thing I've been doing with these Chinese Switcher wall warts,
is checking them for leakage with my Ohm meter. They appear to be Open..