Of course you do see it on public transit in the early and late hours at times, and it's not a big deal, but its definitely not 'normal'. Napping at work is especially frowned upon, with perhaps the exception of someone going out to the park during lunch time.
The general feeling/culture (not necessarily my personal opinion) is that you should have had enough sleep the night before so that you can be productive for the day's work. If you've stayed up so late (partying or whatever) the night before such that you need rest during the day, you're short-changing your employer and teammates. A nap might be the right thing to do to restore your energy, but you should not have put yourself in that position to start with.
Of course these days I don't need to stay up half the night to feel like I need a nap in the afternoon... :)
[edit] After reading the article, I see that the Japanese culture connects the tiredness with working hard/late, which changes the perception. I think in the US and Canadian culture this can happen in some extreme cases - we've all heard (or lived) stories of people working like crazy to meet project deadlines, and sleeping in the office, etc. And road-warriors fighting jet lag are often given some credit for that tired/haggard look. Blue collar workers are more prone to given respect for being particularly tired at the end of the day, but napping or dozing off is still not really rewarded/honored like it seems to be in Japan, because of the quite different work-time expectations.
The real shock for me was when I went back to Canada and realized I'd picked up the habit inadvertently! I would naturally fall asleep in some boring classes and had a lot of difficulty stopping that. Generally the prof would notice and call me out to everyone's amusement, or a neighbor would give me a nudge. It really did not feel acceptable to sleep in class as in Japan.
Honestly, it never really occurred to me that people sleep in public in other parts of the world.
I often see people napping in all of the above, both here in Russia, around Eastern Europe and in South America. And it's no big deal most of the times.
And things like sleeping on the bus/train or sitting on a bench seem to be normal all over the world.
The catch is, i never been to either Japan or USA, so i can't set the zero properly.