Yet Fajo was not unaware of the fact that Data was a Starfleet officer, i.e. somebody who had sworn an oath to kill when so ordered. Data's record, if available to Fajo, would show him at least that Data had readily aided and abetted in the destruction of a number of supposedly crewed threat vessels, not to mention the whole rigamarole of "Ensigns of Command" where Data masterfully bullies himself to victory with acts and threats of harm. Fajo really should have known that Data is both a fluent liar and a trained and practicing killer.
OTOH, there's no obligation for Fajo to let slip that he knows. Pretending to believe the opposite will actually serve him well: Data may then choose to base his clever escape plot on having the ability to surprise Fajo there, automatically leading to failure!
Timo Saloniemi
It's also possible that Fajo assumes that Data isn't capable of cold bloodedly executing a man. When, in fact, Data realizes Fajo is as close to pure evil as they've encountered--cartoonish personality aside.