You're quite right. Overdiagnosis is only important if it leads to overtreatment.
Overdiagnosis actually applies to real cancers. These are not false positive. These are cancers that have been diagnosed on a biopsy.
From that point, the patient is referred for care to a surgeon, to an oncologist or to a radiation therapist. Then her treatment has to be tailored to her. If that woman has advanced heart disease and her life expectancy is short, she will not be treated with the same aggressiveness as a young woman who's in very good health.
We have to screen to find the cancers. Then once we find them, the treatment is decided based on the individual patient, not only the characteristics of the cancer, but the patient's general health, how much treatment she can tolerate and how likely it is that the treatment is going to help her in the long run.
To say that we shouldn't screen because of overdiagnosis means we'll never find those cancers, even the ones that could be treated, even the more lethal ones, and especially the ones in younger women. As I explained, they're less likely to have heart disease and be at risk of dying of a heart attack, so if we do find their cancers, they tend to grow faster and they need to be treated. That's not overtreatment.