That is OK

We do tend to start looking at the wider picture when we cannot locate a baptism or birth registration for someone.
My feeling is that his father was 'invented' on his marriage, especially as at no point he appears to have been living with his immediate family. I can see an Edward R Batchelor in Bristol appearing on adverts for the distribution of wine but he did not die until the early 1900's. Unfortunately not all births were registered this early despite the introduction of registration.
It is strange that in 1871 when he is with the Barber family as a Boarder age 2 his surname is given as Batchelor but in 1881 when he first appears on census in Bradford on Avon with a 'supposed' aunt his surname is listed as Barber before reverting to Batchelor on the next census.