As others have said here, the measurement tools used to screen for CPD and macrosomia (a big baby) are often fairly inaccurate and most women should at least be given the chance to labor and try for a vaginal birth.
Being induced complicates the matter even more.
Inductions often fail when the body is not ready to let the baby out (or baby has not moved into a favorable position). Is your friend being induced for a specific medical reason? It is still within the normal range for pregnancy to go to 42 weeks gestation and often primips naturally go over 40 weeks. Most of our providers won't induce for "post-dates" until the completion of the 41st week (evidence based practice), unless there are other medical complications present (preeclampsia, for example). Hopefully your friend's dates are accurate!
Sometimes, we have patients who are just sick and tired of being pregnant and beg for an elective induction before 41 completed weeks....in my experience, these tend to be the inductions that have the highest failure rate, especially with primips. If there is no fetal distress or other complications going on during the induction, sometimes our patients who end up with failed inductions are sent home to try and wait for labor to start on its own for a few days....and if labor does not start on its own, they come back in for another try at induction later in the week before going to a c/section. But not all hospitals have providers that truly try to avoid a c/section like where I work.
If your friend does not dilate according to plan, her MD may then diagnose CPD and want to section her. If she does have a c-section due to "failure to progress" or CPD, it will be hard to know if her pelvic outlet was truly inadequate. It is always possible that if labor would have started on its own, without induction, she might have been able to have a successful vaginal delivery. We see this all the time in OB. The best evidence of this occurrence are successful VBACs (vaginal birth after cesarean) that had had a c-section for CPD for the first baby. Often these women are able to deliver a larger baby vaginally than their first baby that came by c-section. Of course, there are many other factors at work here affecting the outcome of each delivery, with fetal malposition being yet another common cause of "failure to progress".
Best wishes to your friend