I think the headline is misleading. Let's say I stay up late to do X, Y and/or Z. These things to mean have meaning. In doing them I feel a sense of accomplishment. I've been productive.

Now I show up to work the next day. Certainly less sleep has some effect on me. But that doesn't devalue the increased productivity from the previous evening.

The brain is a limited resource. There might be occasional short term hacks/cheats. But on average you'll have X gallons in the mental tank. This is true. If you spend that at home then yes you will be "less productive" at work.