You have to make a serious effort to be as sleep-deprived as a new parent. You could sign up to have the CIA torture you, for example. But unless you're being kept awake by guys with guns, or you have fatal familial insomnia, you've got nothing on the parent of a newborn. Especially a newborn with colic.
I imagine it's a little bit tongue-in-cheek, not a blanket statement that being a parent is the only way to become seriously sleep-deprived. More like it's one of the most common ways a regular person will experience significant sleep deprivation, so the experience resonates with a lot of folks.
Also, in my limited experience (two kids), the sleep deprivation part isn't really all that bad, unless you're mom. She usually gets the brunt of it. And in any case the newborn phase is done in less than a year for most kids and you settle into an easier rhythm of just mild sleep deprivation :)