I've found marriage certificates to be particularly unreliable because of the public nature of the signing. If someone was illegitimate and married in a different parish, they could have invented a father to match the surname they used.
On the other hand, if the vicar knew them well, they might well have married under their mother's maiden name because the vicar knew they were illegitimate, whereas they always used their father or stepfather's surname through rest of their lives.
I got a new one the other day - I have lots of relatives where the a wife had died and the chap married her sister. This was illegal throughout the 19th century, so the marriage usually took place somewhere else and then the couple returned to their village and everyone more or less accepted it. However, the vicar of this particular relatives's parish must have been a right stickler. Fanny Beer, died and the husband married her sister Jane. When it came to the baptism of the children, the parish records say daughter/son of Jane Beer, a single woman although the births are regstered under the married name and they appear as such on the censuses

Just shows - don't be surprised at anything - people are strange beings

Angela