I studied with Claude Gordon for four years, attended two of his summer brass camps and completed his trumpet teaching course. At the heart of Claude's approach was the systematic development of basic physical technique. Yes, it is true that Claude stated that he did not teach "music". However, he routinely used many etude books in addition to the standard trumpet method books that have withstood the test of time.
Claude's approach was to teach what and how to practice in order to develop prerequisite technique necessary for meticulous and effortless playing. He often stated the well worn quote, "Without technique there can be no music."
If you study only the routines in Claude's books thinking that he designed them as complete in and of themselves, you will be missing out on a lot of other great things. Remember, Claude published his books years ago and did not revise them. Many times while I studied with him he would substitute, delete, and add to the routines contained in Systematic Approach. Concerning one of his other books, Physical Approach to Elementary Brass Playing, Claude said he had rethought some of the supplementary books mentioned in some of the lessons and desired to revise them as he thought they might be too difficult for the majority of beginning students.
Claude wrote his books to fill a void of materials for properly and systematically developing range, breath control and disciplined practice routines. He definitely did not mean to replace Arban, St. Jacome, Clarke, Irons, Smith, Williams, Schlossberg, Gatti, Colin, et al. Like a good doctor he simply prescribed routines from the established medicine and developed his own therapy that tied them all together to cure and/or prevent the student's ailements. If you like you can read Claude's approach to brass playing in his book, Brass Playing Is No Harder Than Deep Breathing.
All of his books were published by Carl Fischer.