When people talk about private lessons, I also take a look at what skill level they are currently at.
I believe that when someone is too new to bjj/grappling, they benefit about the same from a private lesson as they do from normal training. (Meaning a private is just not worth it at that point in their training).
As the student becomes more intermediate/advanced, they are able to notice little intricacies in technique and also perform techniques with much greater precision.
Also, something that occurs is that the student is able to watch an elite grappler, and just an average grappler, and tell the difference right away. Being able to see exactly how the elite grappler sets his moves up/performs differently is crucial when taking a private lesson (in my opinion).
Other than just pure experience, I feel that spending a good amount of time watching matches either online or in class helps tremendously with this.
Now a highlight of Rodolfo Vieira, one of the dominant up and coming heavyweight grapplers