The reason tier II clubs like this field independent AAA teams is because they are losing good players, players that often times they have had since mites or squirts, to tier I because the parents want to chase the letter. By offering an "independent AAA" team they offer a similar experience in that while the team will play league games at the tier II (probably AA) level they will play non-league games and tournaments at the AAA level. This gives the player a chance to measure up against tier I kids, gives the parents a chance to see their kid play a higher level of hockey, and gives the organization a chance to keep these kids in the program.
All this is done while minimizing the ridiculous AAA travel demands and also keeping the cost at or near the regular tier II cost.