I used to do a lot of work in China and what often happens is that factories will over-produce a run and then sell off the excess through back channels. Or they will run a second shift or assembly line in parallel with cheaper materials. They even order extra packaging so everything looks real and legit.
It's rare that they start from scratch to knock-off products, they usually have the plans and bill of materials (or buy them from a someone in the legit factory).
To my knowledge, the only product counterfeiters ever prosecuted by
the Chinese govt were people who made fake Beijing Olympic merchandise and therefore, competed directly with the Chinese government.