Some burners use a flame rod which sends an electric current thru the flame.(to ground) Since most all newer furnaces use electronic control boards to control the motor, burner and other parts, a floating ground can cause problems. Lots of these boards have line filters and such that are referenced to ground thru caps or hi value resistors. A floating ground can produce abnormal voltage reference an cause the CPU to detect problems. Many also have VFD fan motors that will also create odd harmonics on an ungrounded unit. And when I mean grounded I mean bonded to neutral. Odd harmonics or poor freq regulation may also affect the control board. Unlike the inverter AC units these units do not convert all the incoming voltage to DC. Most use a mix of line voltage and control voltage as generated on the control board. I have seen the control board have more components on it than the average home computer. Some use zero point switching on scr controllers that the wave form of some generators have a hard time providing.
