Census are full of anomalies of one sort or another that most people don’t see because they don’t have another document, like an army attestation, to contradict it; indeed I would suggest that many trees built on Ancestry aren’t even supported with primary documents, but have just been built on census and BMD Index entries. The enumerator only wrote what they heard and being human mistakes were made, even the people who were the subject of an entry didn’t always give correct information. Another possibility is the 1881 census people are different to the family you are looking at.
The 1891 census data for William fits with his record (you can obtain a copy of all 5 pages online, see http://www.nationalarchives.gov.uk/records/looking-for-perso...
, so accepting there was no requirement to provide a birth certificate to enlist, it could be a mix up with names on the census.
You’ll have to cross-check births/baptisms (and perhaps deaths) against census for the children and if baptisms cannot be found online it will be a case of purchasing a few birth certificates to sort out parentage.
E.g. William vs Walter b 1861, the GRO Index to birth registrations gives:
GEORGE Walter James, Mar Qtr 1861; District Faversham; vol 2a, page 598
GEORGE William, Jun Qtr 1861; District Faversham; vol 2a, page 613
See if you can find a Walter George birth registration to fit his older brother, and look for candidate for the above Walter James in the 1861 & 1871 census, finally you should obtain a copy of William’s birth certificate; that should sort it out.