That theory has been put forth, and probably has often been true, but it falls down when it comes to state offices -- where statewide, approval rating was in the toilet, yet the same people got re-elected.
There's also the problem of low turnout. In my SoCal town, the same guy has had a monopoly on the mayor's office for years, yet is widely hated. So how did he stay in office? In the last election while I lived there, less than 2% (yes, TWO percent) of registered voters actually voted. Or at least that was what was reported to the SoS office... there were irregularities sufficient that an investigation was scheduled, but nothing ever came of it.
I'm reminded of a tale from the 1972 Presidential election, from someone I knew who was doing a door-to-door survey: When asked their views, most people espoused typical conservative points. But the final survey question was: Who do you think would make a good president? And the most common answer, even from very conservative voters, was "Teddy Kennedy" (then the most liberal man in all of politics). The conclusion from the survey's data was that most voters didn't actually know what a given candidate stood for, but they sure as hell knew the names. (Mind you this was back when most of these voters would remember JFK firsthand.)
Here in Montana, if someone has an abysmal rating, they're likely to get voted out. One might offer a correlation with the much better educational level...