In the short story, Reginald's Choir Treat, Saki writes:

“You are really indecently vain of your appearance. A good life is infinitely preferable to good looks."

"You agree with me that the two are incompatible. I always say beauty is only sin deep.”

What does "beauty is only sin deep" mean? Is Saki implying that sin is required to attain, or maintain one's beauty?