What benefits do training with a trainer offer that the owner can't get on their own?
When I first started clicker training, I can't tell you just how valuable it was to have a good clicker trainer working with me to teach me the RIGHT timing for using the clicker in training. I think with that particular method, the timing is really hard to get right when you are starting and you need to have someone there to tell you when you're doing it wrong and confusing your dog.
That's also the primary reason why I would always prefer to train with other people, even if it's friends who train rather than a trainer - having extra sets of eyes that belong to knowledgeable people who can tell you what you're doing wrong and when you are sending mixed messages. Because when it seems like your dog is "just not getting it", most of the time, the error is on the handler's end, confusing the dog by getting the timing wrong, correcting or praising at the wrong time, having the wrong body language.
I've noticed this especially with trying to work on my heeling. I've actually started using my little camera to film myself to see what my body positioning is when Ronja forges ahead or the distance between us increases and it's not HER at all, it's my body posture and body language.
A book or a DVD can tell you a ton of stuff and you can learn a ton of stuff from it, but it's invaluable to have a second person there (a knowledgeable person) who can watch you put it into practice and make sure you do it right.
IMHO the Michael Ellis DVDs are a great example of this. They're filmed at training seminars. Michael explains and demonstrates the technique. So you'd think people could just do the same thing. Then he shows people IN the seminar who've just heard him explain it and seen him do it, and all the things they do wrong and that he corrects for them to do right.