Another story could be that if the system is working for you, you're probably getting dental, can afford skincare, can splurge on the nice barber, etc.
Attractive people can roll around in mud and refuse to shower for a year and they'd still have plenty of suitors after them. But cosmetic factors can elevate otherwise average looking persons.
They did "control for socioeconomic status", I assume that means levels of costly self-care were distributed across both political aisles when they were setting up the study.