even gopro had a split with biceps the day after back, and I commented saying wont your biceps still be recovering from the compund back movements(pull-ups, bent-over rows) , and he said something like you shouldn't feel it in your bis, you have to pull with your back, if you feel it in your bis u are doing the exercise wrong!
Your arms get a lot of work either way. However, it is easy to cut out a good bit of your back musculature if you don't do the exercise properly. For example, if you don't pull your shoulder blades back together when you are rowing, then you won't train scapular retraction. Really, when people say pull with their arms, they mean shoulders, but your arms definitely help to pick up the slack.
Your posterior delts do most of the work if you're rowing without retracting your scapula. If you pull your shoulder blades back then the muscles running through the middle of your back (Rhomboids and middle/lower traps) get properly recruited. As well, the lats are recruited more efficiently when you maintain a retracted shoulder girdle.
The cue to "pull with your elbows" is just a helpful way to get people to understand what it is to pull their shoulder blades together if their body awareness sucks. A lot of people can't understand the concept of separating their shoulders and scapula as two separate entities.
The only time it's bad to feel the burn is when you're peeing...