To be "fake" these pots would need to be one of the following:
*made in somewhere other than China
*not make of yixing clay
*made after 1940
It's more complicated.
There are fakes, and there are imitations made in tribute. It's been normal practice in Yixing workshops all along to make imitations of famous pots, and to the highest standards.They are all made in China, and often also from Yixing clay.
At all times both were made in China, such as during the ROC period of famous Qing and Ming pots. Those imitations and fakes were often of very good clay and workmanship, and command very high prices as well, and are excellent to drink from. But of course the prices are not as high as true Qing or Ming pots.
But then there are fakes made of very bad clay, or not Yixing clay at all, and artificially aged with materials that can be very unhealthy if these pots would be used.
There are fakes of modern master pots, and fakes of antique pots.
The difference in price between fakes, imitations, and real period pots can be enormous. It's not enough if a pot is just made from Yixing clay, and in China. There is a difference not just in collector value, but also in use.
Many tea lovers only drink from pots made before the change from wood fired dragon kilns to electric kilns. Another difference is the porosity of the clay itself, as it was done differently in earlier times, and many drinkers feel the old by hand prepared clay was better.
That is why, for example, the cultural revolution Shui Pings from factory 1 are so searched after (and often faked nowadays) even though they are mostly not very finely crafted, but used excellent clay done in the old ways.