There was a painful irony to the piece though. By calling people with obesity "obese patients", the New York Times was also not seeing past the fat.
People first language refers to the recognition that people cannot be their diseases. People can have diabetes, they're not diabetic. People can have arthritis, they're not arthritic. People can have cancer, they're not cancerous. And so too with obesity. People can have obesity, they cannot be obese.
The distinction matters. Not using people first language labels the individual by way of their medical condition, and when it comes to obesity, given the incredibly negative societal stereotypes associated with the word, labeling an individual as being obese carries with it real stigma.
At least part of the reason why many doctors don't see past the fat is that journalists, and society as a whole, don't see past the fat either and instead define and stereotype people by their obesity. While it's definitely a small step, if the New York Times (and other media outlets) actively adopted people first language for obesity in their style guides it would be a welcome and helpful change.