Harbor Freight does this, and they even try to associate with real brands. For example their house brand air tools are "Central Pneumatic," obviously similar to the much higher quality brand "Chicago Pneumatic." HF also call their house brand welders "Chicago Electric." A casual shopper might think they had simply misremembered which brand used the term "Chicago," and think they are buying a better quality air tool than they're really getting.
It’s actually a good test to see if you’ll actually need a tool for long. If it works for the one job and you never touch it again, lots saved. If you use it a lot buy the better brand when it dies.