With minimal exceptions, foreign pension income received while living in the U.S. is fully taxable in the U.S. for a citizen or resident alien.
In cases where the United States has a tax treaty (such as Japan), pension income is generally taxed in the country where the taxpayer resides. In this case, the United States. This would explain why Japanese authorities indicated that your wife should pay the tax here, in the U.S.
A quick review of the Japan tax treaty and a few reliable resources doesn't give me any indication of any special exceptions for Japanese pension income that would apply for your wife.
From the link provided in the original post regarding the contributions made in Japan:
Just as with domestic pensions or annuities, the taxable amount generally is the Gross Distribution minus the Cost (emphasis added).
Your contributions and your employer's contributions are not part of your Cost (emphasis added) if the contribution was based on compensation for services performed outside the United States while you were a nonresident alien.
You cannot deduct the amounts contributed while working in Japan from the cost, therefore making the entire distribution taxable.
The Japanese system for taxing pension income is tiered like ours, but backward. The first JPY 3.6 million is taxed at 25% before the rate begins to drop - so, in the end, the tax is likely similar and potentially lower depending on your overall tax rate.
Please note that matters involving foreign tax, especially foreign tax treaties, can be quite complex and this is intended to be a very general overview and not specific advice.
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