" So much of modern Japanese life has been molded by the American occupation."
Very true. But it's also fundamentally different than if the American influence were to have come from 10 or 20 million actual Americans living in Japan.
"Have they not accepted American culture?"
America does not have a culture in the classical sense of the term, or to be more fair - it's a new kind of culture.
Ergo - there is a 'lot less to accept'.
In America, you can 'do as you please' so long as you're not out go hurt anyone.
In Japan, there are a myriad of rules, spoken and unspoken, that one must adhere to.
It's easy for immigrants to 'get along' in the New World.
It'd be exceedingly hard to do so in places with more established classical culture.
This can be seen in Europe: they are very much intellectually and political open to newcomers, and yet have a really, really hard time integrating them.
There are dangerous, 'no go' zones in Sweden.
There are zero 'no go' or dangerous places here in Canada (or at least not based on migrant residence), where we have a lot more immigrants than Sweden.
In Canada we don't have our own language, customs, no cuisine, few social expectations other than fairly secular ones: go to school, get a job, be good, pay your taxes.