Wikipedia: "According to the 2010 census, 58.9% of Japan's adult population is married", "As of 2006, 55.7% of Americans age 18 and over were married."
If you can find the rate of people living with an unmarried partner in the US or in Japan, I'll be surprised because I certainly can't. Part of the reason is that until recently it wasn't even on the census -- only "cohabitating families", which includes living with your parents.
I know this kind of stuff get repeated in the news over and over again, but I'm going to be honest with you. A lot of it is bad journalism. It is popular to trash foreign cultures and hold up your own as superior -- it sells. Reporters get these fluff pieces from news wires (or actually the vast majority of "trash japan" stories start from a single place - The Japan Times) and don't check the facts.
Having said that, if you actually can find the facts, I would be interested in seeing them. I suspect that you are right that people living with unmarried partners (the term currently used by the US census) has a higher incidence in the US than in Japan. But you will have to do a fair amount of work to make the comparison meaningful.
The average age of marriage in Japan is 30.1. The average age of marriage in the US is 28.2. If you couple that fact that 66% of people who got married in the US in 2012 cohabitated for more than 2 years, then you can see that there are a fair number of young people in the US who are essentially married, where in Japan people wait until they are older.
In Japan, that kind of cohabitation is rare (people live with their parents before they get married). One of the reasons (and IMHO, the overriding reason) that Japanese people get married late is because young Japanese women hold a lot of power in the proceedings. Young women live with their parents and work. And even though they often help with costs in the household, they are relatively financially well off. Also, young women tend to want to have children when they are older because it will interfere with their job. Single income families with stay at home mothers is still very popular here. This pushes the age of marriage back. It also pushes the fertility rate down (because if you have your first child in your early thirties, then there often isn't enough time to have many more. Also, it increases the generational gap).
Now, another complicating factor is that in Japan "marriage" is not really a thing the way it is in the west. In the west, marriage is still, by and large, a religious institution. In some countries, only the church can marry you. In Japan, the only thing that counts is having your name on the family register. You don't even need a ceremony. You can just wander up to city hall, fill out the forms and, voila, you are married.
If you are not on the same family register in Japan, you are not in the same family. It does not matter where you live. When the census comes around, it is sent to the head of the family on the register. If there are 2 families living at the same address, then there are 2 census forms. There is no way to indicate that you are cohabitating! Similarly, if you are on somebody's family register (because you got married), but you aren't living together -- there is no way to get another census form! So separation statistics in Japan are also impossible. I even know people who have had a wedding ceremony, but for various reasons did not want to change the family registry. So they are not married! (Which makes things very complicated because all family law is based on the family registry -- if you are not on the registry, then you are not a family, by definition).
Basically, what I'm saying is that you're going to have your hands full if you want to make a meaningful comparison. And like I said, I realise that people are inundated with a lot of stuff from the media (and especially youtube), so it is hard to know what is right and what is wrong. Just keep in mind that quite a lot of the stuff you here is motivated by something other than trying to educate you.