I would be very surprised if the Americans would have carte blanche access to another countries databases to verify what you are saying is true. (and proving a negative is always more difficult). (I'm not discounting that some EU governments could give access, but that would be contrary to the data protection regulations/laws)
Of course they do have access to the airline's PNR data, through agreement with the EU.
I think the value they see in ESTA is that they have the information in advance, and that they retain the right to kick you out (or not let you in) if you lie on your application.