They are a network that is in the boxing business that promotes their business.
I think they cause confusion because the aggressively promote their business and don't try to subtly hide it, which can blur the lines. I do believe HBO is in the boxing business first and foremost. They have a great track record of being good for boxing. They have put of decades of great fights, have pushed for great fights, but because they do have power and control they have pushed their own agenda as well. This type of business plan isn't limited to just boxing or HBO.
Funny because I was listening to my local sports radio and they were doing a segment on minor league baseball and I can see some parallels. The baseball team is their business, but they have to rely on heavy marketing to get people interested. HBO has a very good product, but it doesn't necessarily sell itself like the NFL, they have to create their own hype to get people to show up.
They also IMO put on the best televised product. My biggest complaint of PBC (and I have been consistent with this) is I actually wish their broadcasts were less neutral and more promotion based. The basis of PBC, the fighters, and Haymon may be manager/promotion based, but I feel like their product is neutral and a bit sterile. To me where HBO has succeeded is making it feel like their shows are events and you are tuning into something special. Now of course they are subject to hyperbole and their own self-aggrandizing rhetoric.
This is where Jim Lampley comes in, he is not the most knowledgeable or critical lead announcer (Bernstein is far better), but in terms of managing a broadcast from a marketing perspective and creating an event atmosphere, IMO Lampley is the best I have ever heard for boxing. They have balanced that with other credible on air personalities. Manny Steward was great and probably my favorite technical analyst, I enjoyed Foreman as well, sometimes you had to roll your eyes, but he was good in a Charles Barkley type way. You didn't always agree or knew if he believed what he was saying, but he was entertaining and had plenty of gems. Today, I think RJJ does a great job and is my current favorite analyst from a fighter perspective. Personally I was a fan of Merchant because he never seemed to sell out. Love him or hate him he gave his opinion and stood by it. I like that in a reporter. When Max was hired I loved it, because anybody who knew Max (intentionally bringing boxing to Around The Horn, his raps, and his radio show), knew the guy was a true die hard fan within the industry and got his dream job. However, lately I have been feeling he has been towing the company line too much, rather than play devil's advocate a bit more like Merchant.
Tying it back to PBC, they have the best stable of fighters, the most neutral telecast, the broadest reach of networks, but I still feel something is missing. You never feel that their commentary is anything but average, their presentation is fairly average, and their intro's/ring walks/fighter introductions are pretty bland. If I had my way I would take the sensibility of PBC, but add some of HBO's marketing flair. For PBC that would have been mimicking something more like Showtime, which I am surprised they haven't done more of.