The story I had was 3rd hand, and turns out a little different than I was told.
The owner is a pilot but stays in the back as he does not meet the insurance requirements. The airplane is based near me as that is how they got my name, through the jet pilot grapevine (!). So that would explain why they are looking here, they don't know anyone where they are right now. The usual right seater is unavailable, had to come home for something.
But you said the airplane is based near you? What gives with the long flight and your travel to get there etc. etc?
With the glut of pilots with ratings up their rear ends pounding the streets, something smells about this situation. Not directed to you either.
Had to come home for some reason is a huge red flag all by itself. But back to the original question. I would tell them to take a hike with the normal daily rate as travel and extended time is involved.