Reputable British manufacturers were not the only ones harmed by unscrupulous manufacturers. The practice also covered some US manufacturers as well. For instance, Parker shotguns were a well-known American brand from the 1870s to 1942 and their products were once described as "America's finest shotguns". The company was founded by one Charles Parker in Connecticut. However, any shotguns marked "C. Parker" are actually not made by the Parker company, but are actually cheap Belgian fakes.
A "C.Parker" shotgun. Click on image to enlarge
Similarly, the Henry repeating rifle gained a lot of fame during the American civil war and was one of the first reliable lever-action rifles and a precursor to the Winchester Model 1866 repeating rifle. The Henry rifle was made by the New Haven Arms Company of Meridien, Connecticut, which was later renamed to Winchester Repeating Arms Company, when they started making the Model 1866. However, firearms labelled "Henry Arms" had nothing to do with either of these companies. The "Henry Arms" firearms were either manufactured by Crescent Firearms of Norwich, Connecticut, or by Belgian manufacturers such as Anciens Establissments Pieper or F. Dumoulin.
A "Henry Arms" rifle. Click on image to enlarge.
Such firearms were often called "trade name firearms" or "trade name guns". Large firearm manufacturers would mass produce cheap models and stamp them with any brand name requested by hardware stores, large distributors, mail-order businesses etc. Belgian companies like Ancient Establissments Pieper or F. Dumoulin and US manufacturers such as Crescent Arms Co., Iver Johnson Arms and Cycle Works, Harrington and Richardson Arms Co., Stevens Arms Co. etc. were known to produce the firearms and these were sold by well known retailers such as Sears Roebuck & Co., H&D Folsom, Montgomery Ward etc. Some of the brand names used to sell such firearms include Henry Arms Co., Premier Arms Co., Bayard Arms Co., Eagle Gun Works, J. Manton & Co., T. Barker Co., etc.
Some of these firearms are quite reasonable quality, but they're definitely not high-end firearms and will also not hold up to pressures generated by modern gunpowder loads.