i think you need to talk to the company directly not collection. Tell them to send the bill to american express and explain that they are paying for th loss of uses and administration fee also. may be you are talking to collection dept. only because they do that becoz their concern is to get money from you.  i hope you can settle down the dispute else find a lawyer and get a copy from american express which states that amex is ready to pay for loss of uses and admin fee. i think you might need to talk to the someone who is highly authorise to deal with it.

have a good luck!