Animals are extremely intelligent. More so than we, as humans, give them credit for. It is entirely plausible that a panda would fake the signs of a pregnancy in order to receive better care. Animals have to survive in the wild and they have to constantly adapt to a situation to avoid danger. There is no reason to assume that an animal could not apply similar techniques while in captivity.
I believe that most animals are very intelligent and can adapt to their environment just like human beings can. It would not surprise me if an animal in captivity recognizes and like the special treatment it revived when a certain event occurred. Therefore i can easily see a Panda faking a pregnancy to receive better care from handlers.
While it may seem that this panda was tricking officials at the Taipai Zoo into treating her better, that is highly unlikely. Pandas frequently show signs of pregnancy throughout their lifespans, and per Lisa Stevens, curator of primates and pandas at the Smithsonian National Zoo, "there is speculation that perhaps pandas’ bodies just rehearse pregnancy all the time.” In truth, when a female panda ovulates but does not conceive, the panda will usually endure a false pregnancy that is very difficult to catch.
No, a panda does not know how to fake a thickening of the uterus. However, it is not necessary for a panda to fake a thickening of the uterus to fake a pregnancy. A panda is capable of faking a number of the signs and symptoms of pregnancy even if it does not know the technical aspects.