Before meeting the Doctor, Clara (the un-impossible one, if you want) led a normal life. That most likely includes watching the Moon Landing. Which, as Day of the Moon showed,
included a recording of a Silent post-hypnotically ordering the viewer to "kill us [(the Silent)] all on sight".
In The Time of the Doctor, Clara encounters Silents while visiting the Papal Mainframe. So, why doesn't the aforementioned spoiler kick in, i.e. why doesn't she try to kill them instead of fleeing in terror?