All this talk of tickets not being scanned at the origin. Not an issue with paper tickets.
It's not an issue with cardboard tickets (CCST), but it is potentially an issue with paper tickets (PRT, paper roll) as they have printed barcodes needing to be scanned at barriers.
There have been mentions up-thread that it looks suspicious to exit using a bar-code ticket that doesn't have an entry scan recorded, but surely that must happen frequently by passengers using split tickets? Banbury used to be well-known as a good place to split tickets, so (had the OP bought an additional Banbury to Oxford ticket), how would exiting with that at Oxford look any different from a passenger who had a legitimate split at Banbury? Would the Oxford gateline checker (or RPI) potentially demand to see the tickets used earlier in the journey?