The outlet tester is a "dumb" device consisting of 3 lights wired across the 3 possible 2-wire combinations of the 3 outlet connections. The red light shows voltage presence between neutral and ground, one yellow shows voltage presence between neutral and hot, and the other yellow shows voltage presence between hot and ground. There are multiple situations that will result in the single-yellow indication that the tester manufacturer has chosen to label as "open ground". A floating generator or inverter output happens to cause the same indication, and it has nothing whatsoever to do with an open ground.
All 3 lights being on could indicate an output where both AC lines are hot with respect to ground. Bonding would cause either a graceful shutdown or fried components, depending on the protection circuitry.