Google Maps says it's 4.7 miles between Brighton East Pier and Falmer. Also it's pretty much built up area all the way out to the ground whereas there's open countryside out to Melton. Another point to make is the AMEX stadium is (just) inside the Brighton and Hove council boundary.
It comes down to each individual's perception of what is close enough to Hull and what isn't. Paragon station to Melton is about 10 miles. Munich hauptbahnhof to the Allianz Arena is about 7.5 miles. The Boleyn ground to Stratford is just over 3. MK dons to Plough lane is a shade over 50 miles.
Nope, Falmer is covered by Lewes District Council and then East Sussex County Council. Brighton and Hove Albion is covered by Brighton and Hove County Council. So it's not in Brighton, although the post code is still BN. It's not cheating if the postcode stays the same.
If you stick a pin on the stadium on this map http://ww3.brighton-hove.gov.uk/index.cfm?request=b1120082&node=1576 the AMEX is inside the outermost ward of Brighton and Hove council.