Sounds like a typical watcher of bad youtube demonstrations and now thinks she knows it all!!
Well from a teaching point of view, the three ball method helps a student to create both balance and beauty using an easy method and with manageable amounts of product. Using the three ball method also helps students to appreciate structure and gain more of a three dimentional perspective of the nails they are building. It helps them to learn about brush angles in controlling the product too. We all know that there are other ways of creating nails from one bead to multiple beads and most of us go on to use a combination of all of those methods. I would explain these things, but emphasize the point that this method is taught to HELP students because it is easier for them.
As to using unreacted monomer to smooth out a bead ( which it doesn't ) I would explain that once the bead starts to polymerise, it won't accept more liquid and any excess will cause a very real hazard of overexposure to the client plus excess amount of smell in the working area plus wasting money! It is a very stupid practise.
Is she just thick, stubborn or lazy? If serious about making a career out of nails, then she should read Doug Schoons book re product chemistry which will back up what you say. Hth