Are they really the former US government or are they just a lie?

it just doesn't add up because the Quaere Verum group says there a conspiracy

Good question but I'm not the one to answer it with authority, but considering their Technology and Organisation and there Raven Rock Bunker, I'd say ex-Gov for definite.

Before the war, they were a conspiracy. A conspiracy of many important powerful pre-US people, believed to include the president. They believed the nuclear war with China as inevitable, and the conspiracy was set to allow them, and their decendants to survive it, and rebuild society (Perhaps not on earth, if VB is taken at face value) in their image.

The conspiracy was behind the Vaults, including their secret purpose, and the Oil Rig Facility. The name "Enclave" is believed to come from the name of the Oil Rig facility itself, and taken after the launch. Anyone important enough to be in on the conspiracy was evacuated to the oil rig, where they lay dormant... Until FO2.

http://fallout.wikia.com/wiki/Enclave