3 light testers, surge protectors & other EMS devices cannot actually detect an open ground because they have no way of detecting an open connection between the ground wire & the earth - they cannot reference the earth. Instead, they "look" for the bond connection that usually takes place at the service entrance. If that connection doe not exist, the device assumes that the ground is open.
While a good ground is critical when the power source is the local utility, it is not necessary (or, according to many, even desirable) with a locally supplied source. Floating the system without a neutral bond is allowable by both the NEC & OSHA for 120V low power (under 5KW or so) systems.
Here is an interesting PDF that discusses bonding & grounding of small generators that is worth reading. It explains the reason the utilities ground their systems, and why small portable systems don't always require grounding or bonding.