I find that hard to believe. I see more Honda and Chinese Honda clone engines than anything else, followed by Kohler, Kawasaki, etc. About the only B&S engines I see these days are on 'antiques'.
Remember, “largest” depends on what metric they’re using. It may not be units shipped.
For all we know, they may be claiming that based on “number of square feet in our factory.” :P
Therein lies the problem. A lot of Briggs stuff had been relegated to the lowest end push mowers of Walmart variety.