Yes, you are correct; BAC marked and FN marked guns were all sold concurrently in different parts of the world. How yours got in the US is anyone's guess, but the possibilities are endless. Many guns have been smuggled in by tourists, brought back by GI's or airline employess, or it could have even been brought to the US by a European/Canadian transplant. Who knows?
Regarding the barrel bushing, while (fortunately) it is not too common of a problem, the barrel bushings can and do fly off while being shot (especially if not properly seated), or lost when launched by the recoil spring during reassembly. The style that is on your gun is a late pattern made by FN, and it most likely is a replacement for one that was lost, but it is possible, depending on how close you are to the 700,000 range, that it is original. In general, they are a lot easier to get on and off than older style bushings.
Numrich is usually out of most everything that you need, and Browning hasn't had them for years, but they are out there if you look around.
One possible source is Western Gun Parts (
www.westerngunparts.com ), in Edmonton, Alberta, Canada. Jeff Heimann started out a few years ago selling parts on eBay from his retired father's business (including Browning Parts Distributor), then expanded into a fairly large gun parts company. I have always had good luck with them.
I just checked
www.Marstar.ca website and they are out of them, too.
If you'll also notice, your grip safety is a bit diffferent than earlier guns as well.
I was also going to have you check your trigger to see if it was plastic, but I can see blue wear on it. Some later 1910's have plastic triggers (as well as the FN "Baby" .25's).