Being barefoot means that your skin is hitting the ground instead of plastic/rubber. If your heel lands on a rock bigger than a pebble, it's going to hurt. If your foot lands on a large broken piece of glass, it's going hurt.
Being without the protection of shoes opens you up for increased risk of puncture wounds. This is a trade off that should be considered.
Does correct barefoot running hurt? No, not in the least.
Here's the catch, you can easily overdo it, especially right out of the gate. You can rub your feet raw, blistered, or bruised if you're not adapted, or if your form isn't up to snuff. What would the bottoms of your feet would look like if you had a twist of the leg as you placed or picked up your foot? It would look like someone rubbed sandpaper across your foot thousands of times.
The good news is that pain is the best part of barefoot running. No, not embracing it, but resolving it. Imagine a realtime feedback system that allows you to make small changes and instantly reap the benefits. You may run hours upon hours slightly twisting your leg as you pick it up, develop knee pain, and never track down the root cause, if you're in sneakers.
The same type of thing done while running barefoot will cause pain and abrasiveness on the pad of your foot. It won't take long to realize that keeping your foot straight on ascent and descent removes that pain.
OK, one more time, can barefoot running hurt? Yes, that's the point. I'd rather hurt a little and tweak my form to resolve it then find out later, much more perplexed as to the root cause.