I think their necks swell because of an increase of neck muscles that comes with the "beefing up" they do in preparation for encounters with other bucks in order to establish dominance. It wouldn't make sense that a deer's neck would seem large in relation to the rest of a deer's body, that is, why would a deer's body shrink and not its neck? I have personally seen a deer that had loose folds of skin on its neck due to a swollen neck the previous year with a lack of swelling when the deer was harvested. My personal opinion.