I understand what Steve, Denny, and others mean, but I'm not sure there is an easy answer to fix this.
The award has definitely been cheapened if the outcome is a foregone conclusion, especially when members of each physical club are working hard to have a good showing, and their efforts are swept away by a tide of entrants claiming an affiliation with hundreds of other people they have never met before.
Personally, I'd like to see the AHA require clubs to register with the AHA and pay a nominal per-member annual registration fee (something $5 per member, minimum $200). Only registered members of registered clubs would be able to claim affiliation for the club of the year, and others' claims would be deleted by the software. I think this puts everyone on an equal footing, and while $5 is not enough to pose a real barrier, I suspect it might make it harder for BN to collect and pay those nickels from as far and wide as their fans range.
That being said, I hesitate to recommend anything more radical that would shrink, rather than enlarge, our hobby. I would way rather see thousands of excited homebrewers brought/kept in the hobby by BN, even if it means BN wins the club comp every year, than say bye to those folks.
For example, I would like to be in a club -- and even have several clubs of national standing in my area -- but cannot due to other commitments. Having to ability to make some claim to a community helps, and I've claimed Chop N' Brew as my "club" in smaller comps in the past.