I always ask that vendors charge me county rates for copies unless they can be obtained for free online. I know some searchers upcharge for copies regardless of cost but to me the base fee of the order should account for the time spent, copy costs shouldn't be used on the back end to pad the fee.

I haven't run into a client refusing to pay county rates for copies but I do have a couple clients that wanted flat fees so we averaged out the copy costs and built that average into our fees. Maybe you'll need to do something similar with your client.