You are correct on that point, and I make it all the time, so that is a mistake on my part.
It makes them de facto wiser then, if they have truly conservative beliefs and not just “conservative political beliefs”.
Cawthorn looks like an idiot on this because it is so easy to "bust" him. Simply ask him to name names, and when he doesn't, he looks like he just made it up because he thought the accusation alone would appeal to his constituency.