I can believe that the properties of various metals -- ductility, malleability, etc. -- might dictate tooling & methods of manufacture, which might influence the internal air column & therefore tone. But no, I don't believe that the body of a sax vibrates audibly; it's not a drum or a bell or a ukulele. Granted, I'm neither a metallurgist nor an acoustician, just a sax player who reads science books.
Yep, snake oil. Also called "advertising"... Do you realize that Yamaha's advertising materials actually claim that the plating on clarinet keys has an effect on sound? Do you believe that too, because it comes from Yamaha's ad agency?
I worked in advertising, once upon a time. Some of my bosses & co-workers lacked ethics, but most of us understood that telling lies would be counterproductive; our job, as we saw it, was to tell the truth persuasively.
Sometimes the manufacturer makes a decent product. Sometimes the folks who craft the ads are decent too. Where do the outrageous claims come from?
The manufacturer's marketing department. When they understand neither the product nor the customer, they make stuff up.
Or this happens: I had a client once who came out with a great product. The prototype was stellar, & we proudly devised an epic ad campaign for it in multiple media -- radio, TV, print, point-of-sale. Then the product launched, & to our dismay we discovered that the client was making it out of cheap crummy materials rather than the quality materials we saw in the prototype. The advertising was truthful, yet the product was false.
Just sayin'.