Anthony Yates was christened in Sept 1802, so he could have been born the year before. His parents were John and Elizabeth, and they had 2 more sons in Phillack, Thomas chris 1804 and John chris 1807. Have you found these two on 1841 census, perhaps living near Anthony?
John Yates married Elizabeth Martha in Phillack in 1801, Martha presumably being her surname. Have you found Martha used as a second name for any of the children and can you find John and/or Elizabeth in 1841 or 1851 censuses? If they are still living in Cornwall with another Anthony Yates nearby, this suggests you have the wrong family. Where does your Anthony say he was born on 1851 census? You have to use circumstantial evidence to a certain extent pre 1840-ish, but it's amazing how sure you can be sometimes.