It may come down to your commercial agreement with your customer. I know some customers will ask for more than they specifically require. Understandably distributors won't necessarily want to share manufacturer information for the reason Charles mentioned. I would go back to the customer and assess whether you can persuade them to be satisfied with your certification, or whether they are adamant on having the manufacturers certificate for their own requirement or desire in which case it may escalate to a position of deciding whether you'd rather pass on the certificate or refuse and potentially lose business, depending on their response.
I started out working for a distributor and tasked with retrieving information from suppliers i.e. BRC/FSSC/other certificates, HACCP, SAQ and the rest. Although for BRC we only needed certain information, I had to request everything as the leaders view was 'the more the better'. However if a supplier refused to share something as it wasn't a document we specifically needed to comply with out BRC supplier approval requirements, we wouldn't push it. Hopefully this is the same in your case, and your customer will understand the sensitivity and be satisfied with your accreditation. (Now working for a manufacturer I fully appreciate what an annoying strategy that would be to everyone else).