... apparently a select few airlines (or maybe just Southwest?) will wink at those requirements and allow it.
I have only flown Southwest a few times, but when I did I was surprised how few people were taking carry on luggage. The airline free checked luggage policy opens up the carryon space somewhat.
But with free checked bags, the last time I flew Southwest, my folding bike flew as a checked bag in my S&S Backpack case for free.