TOM - I have had quite a few members in our area who tell us that the "scouting program is the core of the Young Men program." I appreciate what the scouting program offers, but I disagree with that statement. My understanding is that the priesthood is the "core” to Young Men. Perhaps the statement is not entirely wrong, but perhaps the word-use is too definitive.
I have searched in the church handbook, talks, and other supporting documents for this topic. The best I can find is that scouting is a supplement to the Young Men’s program and certainly not the core. Logic also tells me that not every country offers a scouting program. So how could scouting be the core to the Young Men program if many countries do not practice scouting? Although I do acknowledge that in countries where scouting is not available, the church may sponsor its own scouting program.
Any insight you can help me with will be helpful.

JOEL - I would also disagree with that statement. I think that for some people in their zeal to promote the merits of the scouting program to church members they tend to over-sell it a little by saying such things. Here are a few things that have been said in regards to the proper relationship between scouting and the Aaronic Priesthood:

From the Young Men's Presidency:
"At the Priesthood Leadership Conference we focus on how to utilize Scouting within the Aaronic Priesthood. We hope participants leave with a better understanding of the Aaronic Priesthood’s role in a young man’s life and with an urgency to ensure that appropriate Scouting activities are held that can round out a young man in physical, spiritual, social, and educational areas—areas that will prepare him for the Melchizedek Priesthood, the temple, a mission, marriage, work, and life." (Instructing Young Men “More Perfectly” By Larry M. Gibson, First Counselor in the Young Men General Presidency)

From President Thomas S. Monson:
"Scouting is another area of vital interest to young men. Much has been said in the media of late regarding Scouting. Let me affirm that The Church of Jesus Christ of Latter-day Saints has not diminished in any way its support of the Scouting movement. President Spencer W. Kimball declared that the Church endorses Scouting “and will seek to provide leadership which will help boys keep close to their families and close to the Church as they develop the qualities of citizenship and character and fitness which ScoutLDS.org" (October 1991 “Called to Serve”, Thomas S. Monson)

"The Aaronic Priesthood prepares boys for manhood and the weightier duties of the Melchizedek Priesthood. Scouting helps our boys to walk uprightly the priesthood path to exaltation." ( Ensign Nov. 1993, The Upward Reach, President Thomas S. Monson)

And a few statements from President Gordon B. Hinckley:
“Bring into the lives of our young people something more of spirituality. There is more to the Aaronic Priesthood than the Boy Scout program, good as that is. There is more to the Aaronic Priesthood than sociality, essential as that is. Cultivate in the heart of every boy a sense of his relationship to the Lord as he becomes acquainted with the Savior of the world by knowing some elements of the atonement of the Redeemer through which eternal life is made possible for each of us” (Heber City/Springville, Utah, regional conference, priesthood leadership meeting, 13 May 1995).

"Now I am not in any way disparaging Scouting. It is a wonderful program. It is the Church’s activity program for boys in many areas of the world. But I feel that the most important program for boys in the Church is that of the Aaronic Priesthood. Scouting is an excellent and wonderful program that has come of the wisdom of men. The Aaronic Priesthood is a gift from God." (The Aaronic Priesthood—a Gift from God. Gordon B. Hinckley)

Like you I have never heard any church leader say that the scouting program is the most important program or the core of the Young Mens program. And like you said, there are many places in the world where there are no church sponsored scout troops. They would be in big trouble if such thoughts were true. The most any church leader has said is that scouting is a helpful "activity" program to be used to suppliment the Young Men's Aaronic priesthood program.

President Harold B. Lee said:
"May I say to you: Scouting will be successful in this church only as it relates to and maintains a definite relationship with the Aaronic Priesthood. May I put it in a negative way and say that when Scouting fails to be the activity program for the priesthood, it will cease to be a functioning part of the Church program." (Teachings of Harold B. Lee)

Sounds pretty expendable to me if it doesn't do what it's supposed to do. The Scout Handbook says: "Under priesthood leadership, Scouting can complement the efforts of Aaronic Priesthood quorums and Primary classes in building testimonies in young men and boys."

"Complementing" the Aaronic priesthood is a lot different than saying it's the "core" of the young men's program. I suppose we just have to turn a deaf ear to those who might appear to make it more than it is or we can voice our opinion which can be backed up by church leaders. How you handle such attitudes depends on who you are talking to.