This is really embarrassing, especially as I've now been a cat owner for two and a half years, but...
Hair balls aren't "balls".
I thought my cat was one of those weird ones that doesn't really get hair balls! I thought she just had two different kinds of puke, depending on what caused the puke! I thought the long thin dry one that had been hidden and I found later must've been poop! I thought...I don't know what I thought. But, yeah, just recently, I looked closer while cleaning and realized, oh! Lightbulb! This is a hairball!
Totally not a "ball". Hmph.