It really depends.
Last year at Dubai I told the waiter to charge in local currency only being handed a transaction slip that was DCCed - never being presented an option. The dispute process with Chase was a VERY LONG DRAWN OUT process when dispute it online. I believe I have written the incident in length on this thread. (The merchant contested the dispute and refused to reinvoice. Chase sent me 20 pages stack of documents showing the transaction chain from merchant to processor to the bank! Chase offered a $40 credit to a $49 bill but the credit never actually posted albeit I did see it "reflected" in the available credit total, agent who handled this never returned phone call. Long story short, it was a supervisor at the general customer service number took it up and promptly saw the mishap, issued the $40 credit which showed up the next day.

It seems it is much simpler to just CALL to dispute the DCC instead of filing the dispute online despite it has such option to use in the menu of online dispute. Forget about asking for rebilling, just get back the portion being scammed. Friends' experiences have been, a supervisor would simply process the credit on the phone and it is done.