That is strange as their is no difference between shore power connection and generator connection if you are plugging your shore power cable directly into the generator 120VAC receptacle using a RV30A-15A long adapter.
consider this Electrical BLOCK DIAGRAM for typical 30AMP wiring.

I use both connections all the time here using myPD9260C converter/charger unit without any issues.
Hooray for the PD series converters where you can force them into any of the smart mode charging modes by just pushing a button...
Perhaps the shore power 120VAC actual level is alot different then generator 120VAC output level. i.e. one source might be reading 105VAC and the other one reading 125VAC etc... ??
Roy Ken