"My question to all of you who have actually read this far: Is one concept of buzzing any more correct or beneficial than the other?"
More correct? Definitely not. More beneficial? Well, that depends on your own personal preferences and situation. What one person considers to be beneficial the next person will consider to be absolutely "useless". Then there are others who will look at the two and see them as the exact same thing.
Also, is it possible to get any unwanted results from either system?
Of course it's possible. There isn't one correct way to practice - and thank God for that. Each of us has different needs as trumpet players. It is very fortunate for all of us that there are so many different "methods" available. This offers us a greater chance of finding what works for us, personally.
I'm fortunate in that I've written my own books and I've seen how other people have used those books. All of my successful students have embraced my method, internalized it, matured and modified it for their own purposes. In many cases, they have modified it so much that it has become something totally new - far removed from the original influence that I've had on them. Where other people might see this as a flaw in my method (i.e. if my method works, why would they need to modify it?) I see it as a sign of true understanding. My needs and requirements as a trumpet player are never going to be exactly identical to those of my students. Therefore, no one method will ever be completely compatible for everyone who uses it. But with true understanding, my students can share my life experiences and use them to their own advantages, in their own ways.
Applying this to your questions, I think it's good that you're keeping an open mind and considering the effects of different methods, but just remember that, in the end, you have to find what works best for you - and that will most likely be something different from anything anyone else has ever taught you. If it's an intelligent modification, then your own method will be rooted in their influences, but modified in a way that is more appropriate for your own personal needs as a player.
On a final note, I am under the impression that there really isn't an Adam method, not in the way that we mean when we speak of other people's methods. I've never met him but I've read a lot about him, most of it has been on TPIN. My impression is that he has a wealth of knowledge and uses what he needs, when he needs it, in order to encourage the best results from each individual student. So I would be a little concerned about making too much significance out of a one paragraph quote. Adam's teaching is too big, to encompassing, to reduce it to one small quote. I don't doubt that Adam would tell one student one thing and then tell another student something very different, based on the needs of each individual student.
Eddie "Tiger" Lewis