I'm an outfitter on both the Middle Fork of the Salmon and the Rogue River and can tell you about my experience with what you're asking about. (I've heard this called a "row your own."
We generally LOVE having experienced boaters row their own (or kayak) boats along on our trips. There are some liability and licensing issues that we have figured out.
The key is that as an outfitter, we have a responsibility to look out for your safety. We've had some issues with experienced boaters before, so we've come up with some guidelines at:
Some of what we have written might seem a little harsh, but we have had people who are not physically able to row the river which has caused safety issues for the rest of our trip. In short, if you want to row the river, are physically able, and want to be part of our group dynamic, we'd love to have you join us!
We've had several groups of private boaters who enjoyed our trips so much that they now come with us every year or every other year. Yes, booking a commercial trip is quite expensive, but we do all the work, cooking, and take care of logistics so you'll have a nice, relaxing trip.
I hope this helps answer your questions.
Northwest Rafting Company & ECHO River Trips