Professor of psychology here.
Attachment research is full of problems, and I see it as irresponsible for the NY Times to present this area in this way.
Here's the problem: typically, attachment theory and research is focused on a dyadic-level variable as if it's disentangled from the individual-level variables that are part of that dyad. At some level, it's fine to talk about system concepts, but a dyad only has two parts, so focusing on the parts is very tractable.
Why is this a problem? Because a lot of phenomena that are really about the child, or the parent, get folded into some nebulous concept at the dyad level. It's a form of formal hand-waving that allows you to avoid hard questions about who is contributing what to a relationship by simply ignoring the distinction. "Attachment styles" is no better, because now you're just talking about a personality trait as it manifests in a relationship context.
There's more tangible problems with this area of research too, because it almost never sufficiently controls for (1) background genetic and environmental variables together, and (2) individual-level variables that might better account for "attachment".
To be clear, I am not saying that there's no such thing as bad parenting, or that it's all about the child, or that parents don't have any effect. I'm also not even saying that people don't feel attached, or that there aren't relationship-level phenomena. I'm only saying that attachment theory as it currently exists is very problematic theoretically and methodologically. Criticizing such research is politically very unpopular (because doing so leads you to be cast as anti-child or anti-family), so the field persists.
It's very much in the same ballpark as psychoanalytic theories in the 60s: something that is fundamentally flawed, but has a kernel of truth, so becomes ubiquitous.
My advice is to approach your child as a parent, as you think best under whatever circumstances you find yourself in, and don't worry about attachment--it's an epiphenomenon.