http://www.scouting.org/scoutsource/CubScouts/resources/CSLeaderRecAwards.aspx
"tenure used for one award may not be used for another."
and
Cub Scouter Award
Tenure
Complete two years as a registered adult leader in a Cub Scout pack.
Training
Complete Fast Start training, if available for your position.
Complete This Is Scouting and specific training for any Cub Scouting position.
Complete Youth Protection training.
During each year of tenure for this award, participate in a Cub Scout Leader pow wow or university of Scouting, or attend at least four roundtables.
Performance
Do five of the following:
Assist in planning a pack program that results in advancement in rank by a minimum of 50 percent of pack members each year.
Serve as an adult leader related to a pack that earns the national Quality Unit Award.
Serve as leader of a blue and gold dinner, pinewood derby, space derby, raingutter regatta, field day, picnic or other Cub Scout pack activity.
Give leadership to a promotional effort that results in at least 60 percent of pack families subscribing to Boys' Life magazine.
Develop or update a Tiger Cub or Cub Scout den activity book listing local places to go, things to do, costs, distances, etc., for the five Tiger Cub areas, or for at least 12 Cub Scout themes.
Give leadership to planning and conducting a pack service project.
Organize participation of a pack in the Cub Scout Academics and Sports program.
Help conduct two annual pack Friends of Scouting campaigns.
Serve as a leader for members of your pack attending a Cub Scout day camp or resident camp.
I read it as any "registered adult leader in a Cub Scout pack", so yes den leaders can qualify for this award.
Either case, only one knot should be worn per award earned, and maybe for fun give them a copy of the Insignia Guide. He may not realize he is in error with the knot.