My company (of which I am the President) has an account with Enterprise.
We book the cars for our staff, the staff collect the cars, and we get an invoice on return.
The rental agreement is always with the renter in their personal capacity.
Billing of the rental + any unpaid extras (one way fees, fuel, etc) are invoiced to us at the end of the rental. They don't give a credit card and we stand as garantor for the damage excess.
However, any offences (speeding, parking...) plus admin fees are passed directly on to the driver, our company has no involvement with them at all. Payment is between the driver and Enterprise directly.
I don't object to them levying an admin fee (it was in the contract). What I do object to is their confusing procedure, whereby they say :
1) Here's a parking fine. We won't pay it, and will pass the details on to the council. You'll be able to appeal once they contact you.
Then a couple of weeks later....
2) Actually, it's too much effort to insist you were the hirer, so we'll just pay it, and sod your right of appeal.