That's odd, what if simply a high-level of sodium reduces your perspiration? Wikipedia[1] says "The volume of water lost in sweat daily is highly variable, ranging from 100 to 8,000 mL/day." so between 0.1 and 8 liters per day! [2] even says 10 to 12 liters per day!
If on average over a long period the subjects drank let's say exactly 1 liter per day and peed strictly more than 1 liter of water, then I'd agree with what this Dr. said, but neither this nytimes article, nor the 2 papers mentioned [3][4] mention the word perspiration or sweat in their abstracts/summaries, why not?
Off-topic: Did nytimes.com made it hard on purpose to select text from their article? On Chrome and Firefox I can't select text easily, only Edge lets me.
[1] https://en.wikipedia.org/wiki/Perspiration
[2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2267797/