Just to point out:
The person you quoted did not specifically say they meant "USA" when they said "America", although that was what they meant. What if his initial post had actually meant those of us on the American continents, and not just USA?
At any rate, it's just a name. There's no real use to getting worked up over what people call themselves. After all, what would be a good alternative? USAer? You have to remember, too, that English--like many languages--shortens and abbreviates words and phrases. Australians are Aussies, Britain citizens are Brits, United States of America citizens are Americans.
Yes, America also extends to other countries that don't have "America" in their name, but belong to this same continent, but if you understood his initial post as "Americans" = "USA citizens", then it shouldn't be anything to go out of your way saying those in the USA are greedy with the American name. It's usually understood that what the shortened term "American" refers to. I'm pretty sure those in North Korea don't get upset when people call South Korea "Korean". Well... actually they might, haha.
Anyway, if there is any real problem, you should tell people in Japan to stop referring to USA citizens as アメリカ人 [amerika jin] rather than アメリカ合衆国人 [amerika gasshukoku jin].