Seems to be something screwy in the input circuitry then.
Do you have an adjustable power supply? You could try to use the function generator to generate a sine and then increase the negative offset with the power supply to see if/when it starts clipping.
I generated a 60hz sine and added a DC offset which I gradually increased to 20V. I didn't see any clipping, hmm...
Oh, and the clipping on the scope happens with a positive offset as well. With the wires reversed, it's just a reflection about the time axis.
Was PE from wall/mains socked/similar used for configuration #1?
...
BTW what DMM says in both cases?
For #1, ground/earth was from a mains wall socket, after I compared it with a few other sockets to make sure there was nothing funny with it.
With a DMM for #1, the offset signal (blue) measures 10.4V RMS and +15VDC. The yellow measures 14.28V RMS, -130mVDC.
For #2, I get 3.3V RMS and -14.4VDC.
Seems fine? This is with both a dedicated DMM the one built-in to the scope.