If that were true, Carter and Clinton never would have been president. Candidates on the left who pretend to be centrists win elections if they dupe enough fools into voting for them.
That's exactly what happened in both cases. Carter was considered a moderate in comparison to McGovern, Humphrey, Udall, etc. No, he was no Scoop Jackson or George Wallace -- but that wing of the 'Rat Party is gone and the 1976 Carter was pretty close to 1992 Zell Miller. Carter himself has drifted Left since his political demise in 1980.
As for Bubba, he invented running as a centrist. He came to fame via the DLC. After the 1994 debacle, Morris convinced him to head more towards the center. In fact, his signing of welfare reform was more conservative than liberal.
I had no use for Presidents Carter or Clinton, but they governed much farther from their Left Base than Bush is from his Right.