Hi there,
I am attaching a snip from the 1856 parish register. You will notice that the clergy did record the information that the groom provided about both his own parents, and that part of the details are still there on the remaining part of the actual page which has sustained damage. The image is extremely difficult to read, so too are other images on pages before and after that one due to that damage.
If this were my family I would continue the conversation with St Peters and gently ask them if they can confirm that the Rev'd did follow church rules re keeping two registers concurrently, and if so, can they check for the location of the 'other' one. Both registers meant to be kept separately from each other, and both meant to be kept secure, and away from fire etc. It seems to me that it is highly unlikely that the 'other' register would have sustained the same damage to the same records, and so depending on how determined you are to obtain the names of both parents, and how patient you are, I think you are quite close to solving it. Sydney Diocese may well be the custodians of St Peters registers.
PS, for example, a clergyman may keep one register within the church building's secure room and the other in the fireproof safe in the manse - so they are in two separate locations.
JM