Ok - now I am going out on a limb and give some OPINIONS based upon my experiences, both as a player and as a repair tech.
The theory of the air column is fact. No arguments there, however it is my OPINION that once the column of air resonates, it transfers the resonance to the metal body tube (and bell, and neck). The resonating tube, then re-affects the column of air in the tube and changes the character of the sound. (NOTICE I DID NOT SAY "TONE")
I can give one clear example (in addition the the many subtle ones that would take to long to explain here).
Years ago, my 1969 Buffet SuperDynaction Low A Baritone was my main horn while studying at SUNY Fredonia. The bell to body brace is the same design (and size) for the Alto, Tenor, and Baritone. This resulted in a brace that is too small for the large bell of this Low A saxophone, and thus it broke.
I had it soft soldered when I was in college. It broke again. Well, after a few times of it breaking again over the next few years, I had enough, and as I was apprenticing at a repair shop, I decided to fix it right. I took off all the parts of the brace, silver soldered them all together, then put them back on the horn as a one piece brace.
Now, here is where it gets interesting. Over time, the weight of the bell bent it slightly forward, so in order for the brace to be attached needed to be bent against the natural spring of the situation at hand. This is how it had been since the last repair, which means the brass of the saxophone had constant strain at that point.
When fixing this problem now the correct way, I straightened the bell so the brace fit between the bell and body with very LITTLE pressure holding it in place - thus no strain or pressure on the brass.
When the "fix" was finished and the horn was re-assembled - the resulting resonance was astounding. Again, not change in sound, but change in resonance. The old brace attached under tension, hampered the transfer of free resonance in the body tube from the air column.
I will also add that later in life I had this horn silverplated. Again, sound did not change, resonance did however.
It is MY OPINION that things that impact the secondary resonance of the body (primary being the air column) , are perceived by the player as a change in sound - but in reality are a change in resonance.
OK people, I am ready for you to hang me at the old oak tree for these opinions now. I will bring my own rope and black hood.
Charlie