This is an interesting article and my impression is that there is A LOT more to this story. I suspect there are many layers to this, and it reflects the complexity of the current health care situation in the US quite well.
There is a growing movement in the US to reject "conventional" medicine. This is especially true for the field of obstetrics, where I DO believe there has been significant harm to women and babies from a patriarchal, antiquated system. (That's a lengthy post on its own topic.)
The answer, however, is not to pursue freebirth or reject care entirely. (Freebirth is the practice of having no professional support during delivery and often throughout the pregnancy, including the use of a midwife. It is incredibly risky for both mother and baby.). This mother, because of her background as a doula (no formal medical training for this in the US) opted not to see a midwife until her third trimester, something which is highly unwise and makes me question her judgement. Her preterm labor may very well have been prevented (or at least anticipated with a plan of care in place) had she been followed by some sort of a practitioner earlier in pregnancy.
Once a mother presents to a hospital in preterm labor, it's a high alert situation. All hands on deck, ready to help that mother and baby. The well designed birth plan or low intervention delivery goals can fall to the wayside, especially if there is fetal distress.
Having discord between the mother and the care providers escalates emotions--on both sides. I've been on the receiving end of parents who are refusing medically necessary interventions and it's very challenging. I've had colleagues lose their tempers or have moments of unprofessional behavior when they feel a child is being harmed by a parental choice. It happens; physicians are human, too.
I can understand her desire not to have a male examine her. Under planned, calm, or normal circumstances, I strongly feel hospitals should honor this request. However, in an emergent situation, it's possible (especially in a semi-rural hospital as this appears to be) the male resident and attending were the only OB providers available. Again, prenatal care throughout the pregnancy (with a midwife or OB) could have identified a concern earlier on and prevented this from occurring.
Delivering a preemie is very different than a healthy, term baby. We whisk the preemies away immediately to ensure their vitals (especially breathing) are stable. Minutes lost here can result in damage to the brain or even death. Every second counts. Waiting for the cord to fully stop pulsating could have significantly threatened this infant, and I feel the mother was foolish to make this an issue. She is fortunate her baby is doing so well; I've attended plenty of births where the outcomes are much less happy...
Refusing vitamin K was also not based on a sound understanding of the evidence. The wording in the article really made me angry. It is incredibly safe and yes, it IS lifesaving.
In some states in the US, the law mandates that refusal of vitamin K (or the antibiotic eye ointment or hepatitis B vaccination) results in an automatic call to child protective services. (I don't necessarily support these laws, but they do exist. I did not have erythromycin put in my babies eyes at birth, but fortunately, my state does not require I be reported.) Many states stipulate that parents sign extensive waivers indicating they understand the risks and still decline the treatment, which can be perceived as "pressuring" or "coercion," but is again a matter of state law.
Bottom line: we definitely have issues to deal with for obstetrical and neonatal care here in the US. (It's a broken system and we have a sicker population here.) But this mother's judgement does, in my opinion, seem to be lacking and I feel she seems to be lost in a very one-sided view of her experience. The overwhelming majority of physicians, nurses, midwives, and mid-level practitioners in the US care deeply for their patients and are not out to punish mothers.