"Exercising was said to be useless, since it was purported to be scientific fact that a person would have to walk at least 30 miles to lose a pound. The converse, that walking 1 mile a day for 30 days would keep a pound away, was for the moment conveniently ignored. Time magazine quoted a physician at an AMA meeting in Chicago as stating that to lose a pound, you would have to climb the Washington Monument 48 times or do 2400 pushups. What was the point?"
There are a variety of things that could be done with these sentences. I'm not going to get into whether or not there really was a physician who said that at the AMA meeting.
Strictly speaking, I don't think that converse means what the author used it to mean. More or less like I don't think the NPR author meant "exponentially" in its strict sense a few days ago. Whatever.
The author says "purported to be a scientific fact" that 30 miles = a pound worth of calories. Purported is technically correct in the sense that that's what people were saying but 30 (flat and a relatively good surface) miles really _would_ take off about a pound. Then she _does not_ say "purported" or "alleged" or "was believed to be" when she quotes the AMA meeting attendee saying 48 times up the obelisk = a pound. Which _it does not_. As near as I can tell, 48 times _up_ the obelisk would = a pound and a half or thereabouts. 48 times _down_ the obelisk would equal about half that -- call it three quarters. 48 times up and down (since you can't really repeat one direction any other way) would equal over two pounds but probably less than three, assuming you kept level hydration throughout the process. Which would be tricky.
I sort of wonder about an author writing about diets that uses purported and converse and doesn't point out the suspiciousness of that obelisk calculation. Just because you're writing history doesn't give you any excuse for sloppy writing or innumeracy.