With all the lawsuits against the cops these days..... it's really no wonder that they stood back and did nothing.
If they had gotten involved, and the guy had died, they would have been defendants in a law suit. As long as no laws were being broken by the guy in pain.... and apparently it wasn't a gun shot victim, standing by waiting on the rescue squad was all they were required to do.
I'm not defending their actions, just observing that we didn't have all the facts in the story. Was the guy bleeding? Had he been stabbed or shot? Did he have a medical problem? Was he spaced out on some sort of drug cocktail? Was he an imminent danger to himself or others? What was the race of the guy and the cops? Apparently the NYPD didn't think he was in need of their expertise and decided to simply wait on the medics.
As a trained Search and Rescue technician, it was drilled into our heads that we're under no legal obligation to assist someone and especially if the assistance will put us into immediate bodily danger and if what we would be doing exceeds our level of training. That last one is crucial. If you're not trained and certified in something....You don't do it. Period. Lawyers absolutely love asking what training and qualifications you have to do what you did or attempted to do. If you have no training..... that's a question you don't want to have to answer in a court room. Life and death situations exempted, but this doesn't sound like L&D the way you describe it.
My guess is they played it by the book.