They went after some details that would require actual JAMA access.
"But among the study’s other problems, Dr. Briss said, its subjects who seemed to consume the smallest amount of sodium also provided less urine than those consuming more, an indication that they might not have collected all of their urine in an 24-hour period."
NYT says Staessen is the lead author, which sort of made me scratch my head. He's the last listed, an important spot -- but not the first spot, which is what I understand "lead author" to mean. I think Staessen may be a bit of a media ho, and would prefer to demonstrate that high blood pressure is an artifact of heavy metal poisoning rather than salt in the diet. I have mixed feelings about including a bunch of quotes from Alderman, since he was shilling for the Salt Institute at one point, but NYT does include that which might have the (desirable) effect of making everything he says extra suspicious in the minds of alert readers.
NYT does _not_ point out (and I wish they had) that the "low" sodium tertile in the study was consuming about what is recommended for a "normal" diet -- it wasn't anywhere near what a "low sodium" diet is considered in medical terms.