I'm not sure that's correct for primaries.
Primary elections are by party, so are by definition more extreme than general elections. A candidate must win over an average Democrat OR and average Republican, not an average across all voters.
Further compounding the problem, many states/districts hold closed primaries and/or caucuses, which limits participation to those with a strong interest in elections (either enough interest to join a party and/or enough interest to give up half a day or more of time to join a caucus).