Historically, this has often been an Invoked Trope, letting rulers shift the responsibility for screwing up. The common people are more likely to blame advisors than rulers for bad decisions, confident in their belief that it must be the evil advisors and ministers who hide the truth from the benevolent ruler.
This was especially common in monarchies, where the hereditary rule was seen as an expression of divine will. For instance, in 19th century Russia, the peasants commonly thought the Tsar was on their side, passing the blame for bad laws on their favorites such as Arakcheyev, Shuvalov, Pobedonostsev, or Rasputin; the Romanov dynasty ended in blood when it exhausted this credit of confidence and the people came to blame the Tsar himself for two lost wars, suppressing peaceful demonstrations, and generally not caring about ruling the country.
Oh, and since Adolf Hitler was commonly known as the Chancellor of Germany, specifically while Paul von Hindenburg was still alive as President, allied propaganda had a field day with this trope, and may be one of the reasons why we often see it in media.
Historically a lot of "powers behind the throne" be they the magister militum in the late phase of the (Western) Roman Empire or the cardinals and advisors that ruled for Louis XIII and Louis XV (and during Louis' XIV minority) had no major dynastic ambitions (though the Karolingian dynasty of the Frankish Empire did start out as "advisors" to the Merovingian kings) and hence were easy to paint as evil after their demise - even the works of Shakespeare show a bias to portray kings who were ancestors to those in power during the Bard's life positively while skewering their rivals - if some cardinal Richelieu has no (acknowledged) descendants, it is a much easier game to play to paint them in the most garish colors than if you're writing about the great-great-grandfather of the current king, who might be your employer. Of course modern historiography has somewhat cut through the BS, but there is still a lot of myth in popular perception.