I never heard about Bully Sticks until I read about them on Yorkietalk, and so many people recommended them that I did a search and read many articles on their safety. I concluded the same thing as your vet, not all bully sticks are created equal. We've had several threads here about Bully Sticks possibly connected with diarrhea or infection, and they were always a generic brand. If a bully stick has no artificial preservatives, it's imperative that they are dried property, and the moisture content has to be extremely low in order for bacteria not to rapidly reproduce. I don't recommend bully sticks that have artificial preservatives either, because they have a "shelf life" and there are reports of dogs becoming sick from bully sticks with expired expiration dates, also why use artificial preservatives, if there is an indeed safe way of naturally preserving? Drying is a very safe way of persevering meats, but it must be done, in carefully controlled circumstances.
I only buy Merrick Bully Sticks, and they are made in the United States, under carefully regulated conditions. They are more expensive than imported brands, but I believe they are so much safer, according to all the antidotal stories. I think people are misled by the words "free range cattle," and think the product might be better or more humane for the cattle, but this too is misleading, free range doesn't always mean more humane, it could just mean no fences, and no regular food, and it says nothing about the safety for our dogs. Also, a bully stick that is dried thoroughly with a low moisture content, is not only safer, but it lasts much longer than one with a higher moisture content, so in reality, a premium bully stick is really not that much more expensive. Joey's been chewing on Merrick Bully Sticks for about 4 years, and I believe they are very helpful in keeping his teeth and gums healthy. He's never had diarrhea either.