I, too, have several of Paul Bragg's books, and I have benefited from them. I don't doubt the good health advice he dispensed throughout his life helped many.
The People magazine article claims he "had wrestled for the U.S. in the 1908 and 1912 Olympics". I cannot recall from my reading of his books him mentioning that he was an Olympic athlete. He did seem to like to toot his own horn, and I find it hard to believe he would have failed to mention that fact. An online search of Olympic rosters from the 1908 and 1912 games does not show a Paul Bragg as a member of the U.S. team.
If he was not a member of the U.S. Olympic team and he allowed People's assertion to stand, that's akin to claiming to be a military veteran when one isn't. That doesn't discredit all the good works he did, but it certainly a blemish on his record.
The Mat.com - The Official Website of USA Wrestling
United States at the 1908 Summer Olympics
United States at the 1912 Summer Olympics