No, it makes perfect sense. If you get paid per mile then you are buying the fuel, nobody else is.
Exactly, the payment and break even point is irrelevant.
I pay £60 for a tank of fuel. I'll drive the car dry. Within a week ~£160 is in my account to cover the fuel and general wear and tear accumulated for the mileage covered.
Whilst I have physically paid for the fuel at the point of receipt, I am reimbursed for it - it seems like you're arguing semantics in the name of pedantry here as the reimbursement is intended to pay the fuel cost and additional wear and tear.
To my mind, the break even point is entirely relevant because I am only out of pocket when the total cost of running the car exceeds the total reimbursements I receive for doing so in the course of my employment. That is when there is a net cost to me as I am worse off than I would be if I didn't have the car (or didn't use it for business). Any payment above what the car costs me to run is a net gain for the same reason.
This is why talking about my driving style's lower MPG being a net cost to me make no sense. There is an opportunity cost in that I have to make a trade off between a greater net gain via reimbursements and driving quicker, but a net cost it ain't because, barring a calamitous failure of some kind, the car can be well maintained, fueled, taxed and insured for significantly less than £4,000 a year (assuming a minimum 10k mileage at 40ppm).
I can't help but feel this has gotten way out of hand, despite being near enough irrelevant in the first place.