interesting discussion. Cant remember source but suspect Homer Tylers Browning .22 book which is now collectible. Trombone patented in 1919 but sold to Remington (model 12 .22) so they could not be made or distributed by Browning in the USA. Prime markets for FN produced were Canada and Australia (all of Europe) and 150,000 produced up until 1973 when Browning left Belgium in favor of Japan. First order with FN in 1922 was for 10,000 units so my first year production ser# 54xx was from late 1922 or early 1923. My ser #94xx is dated at 1923. They a made a lot before 1930 and I have seen on a CGN thread that ser # 27### could be either 1926 or 1928.
There is one article/booklet which supports what you say albeit slightly differently. It says that Browning & Winchester had an agreement, Winchesters for the US market and Browning Trombone for the remainder of the world. The Winchester Model 63 comes to mind.
I wrote to Browning and asked them about this and I received a phone call (nothing in writing!) and their spokesman absolutely denied such an agreement ever existed. Nobody wants to run afoul of anti trust laws.