Zapper I think the factor that matters in regards to your question is whether an FN Browning is the same thing as a "real" Browning. And the fact of the matter is that the "real' Browning was the one built by FN.
That is what the Belgian Browning built for most of the 20th century is, the gun built for the Browning Company by and under contract with Fabrique Nationale of Belgium (FN). The one above was built in the same factories as the ones badged Browning and sold here by the Browning Company. This one just (presumably) went to the European market.
The Miroku Brownings came late in the game, and the Remington Model 11s and Savage gun were not Brownings, but built on his patent again by contract. I think there were other browning patent guns built by others, but the only one that is a true Belgian Browning is the FN product.
The story I have heard is that after Winchester did so well with its Model 97 pump built on John M. Browning's patent he tried to sell Winchester his patent for the semi-automatic gun, what became the A-5. Winchester seems to have rebuffed Mr. Browning by making him wait for some time to see the Wichester president.
Mr. Browning waited a while, the put on his hat and his coat over his arm and went to the Telegraph station and wired Fabrique Nationale to see if they wanted to build his new gun. The rest is history and the Belgian Browning was born...Geo
or something like that; I'm sure Researcher or someone will correct my post.