I've been looking into the anonymous brand behind Furbish, Baby Brainy and Gigabot.
An idea struck me to try looking up the barcodes seen on their boxes, which pointed to a Taiwanese company called Pro-TV: https://official-furby.fandom.com/wiki/User_blog:Zavsegdataii/Furbish,_Baby_Brainy,_Gigabot_vendor
This might be the real supplier for those fakes. However, I believe that the actual manufacturing was contracted out to companies in mainland China since that appears to be the cheapest and most common approach.
Since so many fakes share the Furdish-speaking program, it is well possible that there was a single Furby clone design that was licensed out to companies like that one and Teamforce.