The question at had is "Is it responsible for a parent to let a 12-year-old child ride the NYC subway alone?"
Honestly, I don't understand why this is even controversial. There is no rational reason to suggest that letting a twelve year old ride the subway in New York is categorically irresponsible. In fact, if the child is not able to ride the subway by the age of twelve safely, this suggests in my mind either developmental problems in the child or severe flaws in the parenting.
To be sure, parents like myself have many worries about leaving children outside our immediate supervision. However, learning to be responsible in an adult world is an important aspect of childhood, and children who do not learn these things when they are reasonably fearless will be handicapped in learning them later. Certainly, too, there are many parts of the world where I would not let a child travel alone on public transit. However allowing children to become more independent and face acceptable risks themselves is helpful, provided the risks are, of course, acceptable.
So the first question is whether the risk is acceptable. In my view, such an approach should begin by looking at the major concerns, and use statistics to see if the risk is acceptable.
The first concern is that the child might be abducted and be the victim of a crime. However, according to Christopher Beam, writing on Slate (article dated January 17, 2007), although 800,000 missing persons cases are filed for children every year in the US, very few of these turn out to be stereotypical kidnappings. Most are cases where the child may walk away unsupervised, runaways, and so forth. Additionally, around 200,000 of these are family abductions, and only 115 cases per year are stereotypical child abductions (the rest of the abductions most likely involve closer contact with the victim and family members). To put this in perspective, nearly twelve thousand children are killed in car accidents every year. Yet, although nearly a hundred times more children are killed while riding in a car every year, nobody thinks twice about driving to the store with the kid in the car. Stereotypical child abductions, while they do happen, are sufficiently rare to be discounted as a real risk.
A more major concern though is that the child might get lost, leading to further problems, traumatic experiences, and so forth. This is a more reasonable concern in that it is hard to quantify how big the risks are. Furthermore nobody doubts that letting an unprepared child of any age ride the subway alone is a bad idea. However, the risk of getting lost can be both substantially reduced and mitigated. While I think that parents who don't make efforts to reduce and mitigate this risk are irresponsible, that is a separate question. At very least, children should demonstrate an ability to navigate the subway system, and should know how to contact the parents if there is a problem. At the same time, I don't see why a child as young as six, seven, or eight who demonstrates these things couldn't safely ride the subway provided the risk is also mitigated by having a means to contact the parents. Such a means might include a cell phone, money for a pay phone, knowing who to ask for help (such as law enforcement officers and transit authority staff), and so forth. The specific approach to mitigating this risk will be up for the parent to decide.
Certainly I think that it is possible to irresponsibly allow a child of the age of twelve to ride the subway alone, but I think it is also quite possible to allow children that age or even much younger to ride the subway alone responsibly, provided that the child is properly prepared for the experience. I would expect that properly prepared children would be less at risk in riding the subway than they would be riding in their parents' car (a risk almost everyone believes to be acceptable).
We shouldn't rob our children of independance because of our own insecuries or delusions. Instead we should take a sober look at risks as they appear, determine if the risks are acceptable, and approach them appropriately. While children shouldn't be insulated from all of life's risks, they can and should be encouraged to face them after being properly prepared.