COA's have their place in an items history but of course they are not the final word on authenticity. For instance this recent Julien's auction item, Lot 951: MIA FARROW "ROSEMARY'S BABY" WORN NECKLACE. According to the auction description, the necklace was screen worn and consigned by Miss Farrow, yet it doesn't appear to match the screen worn necklace in any screen grabs I viewed on Netflix.
It does appear however, to match a replica of the necklace currently available for sale on Etsy, which is different then the one seen on screen. It looks as though Julien's eventually pulled the item as there is no for sale price listed after the auction.