I kind of understand what you mean, but it seems to me the easiest thing is to make one phone call to fix it, not two ...

If you let the merchant try to fix it first, in the worst case you still make the same two phone calls you would have made anyway if it isn't fixed by the merchant (one to the merchant, one to the credit card company) ... best case you only have to make the one phone call to the merchant and don't have to call the credit card company and expalin it to them (and provide whatever documentation they're going to want, which varies by credit card company, and admittedly is sometimes not required).