I don't get airline miles with one of my CDP's I use so I put down Hertz ZE1 pts when I use that CDP.
If I have an inexpensive rental, I will use a different CDP that does not discount as much but allows me to get Virgin Atlantic miles. (1100 per rental with my 5* status). I may pay $2-3 dollars more but get well over $11 of value (probably more if I value a Hilton pt at greater than 0.5 cents--1 Virgin mile equals 2 HH pts

).
Since Virgin Atlantic is a foreign airline, there is no FF fee.
Bottom line: I would put down Hertz ZE1 pts and see if you get those. Your results "mileage" may vary. (YMMV).