As I think of them:
1) Many.. far too many.. people want their tree to be massive, so they will grab info without actually checking for accuracy. 1% of the tree made an error, and the other 49% GEDCOMed, and added.

2) Have you checked on his marriage record for the name of a father?

3) He may not have been born in Wiltshire. If he was the eldest he may have been born where his mother was from (eg: different county)

4) The baptism may have been destroyed by time, rodents, water, fire... Bishop's transcripts may have a backup.

5) Where is he in 1841? Are there older BATTENs around him who might fit the bill? Are there any BATTENs near him who may be his brothers?

6) Are there any BATTENs as witness on his marriage record?

7) William may have been a middle name he ended up going by, or the name may have changed for some reason. I have several people in my tree who did just that. Mostly the name change seems to be to honour a deceased relative, but there is also the event that the name was the same as the parent, so to avoid confusion the second name was used.

8) Is there an obituary? Does his death record mention the name of his parents?