What information James Walter J Eves chose to give about his father on his marriage was up to him. There were no checks in the sytem to see if the information was incorrect. Illegitimate people for instance in particular fabricated father's names and occupations so there were no questions asked about their legitimacy. You therefore cannot rely on information given on marriage certificates particularly where there is no other evidence to be found to support that information.
On the 1891 census James gave his name as Walter not James, but with the same birth year and place of birth - so Walter/James was consistent with that information which he also gave again on the 1901 census.
Why do you think he might be giving incorrect information about his birthplace on these two censuses?
Did James Walter's third initial on his marriage - the letter J - stand for John?
How have you eliminated the Walter John Eves birth registration which is in the correct registration district for Strood and also registered at the correct time for your Walter's birth?
What information does this birth certificate give that makes you think it should be eliminated as a possible?
Walter John Eves seems to disappear from records after his birth, while meanwhile Walter Eves or James Walter J(ohn)? Eves appears for the first time in 1889 marrying in Shoreditch and then with his family as Walter in Frindsbury on the 1891 census.
When women marry/remarry their children from previous marriages or relationships can frequently appear on censuses in their stepfather's surname only to return to their original surname when they leave home as adults. Have you managed to rule this possibilty out for your Walter/James?
Regards
Valda