Japan's per-capita GDP today, even after 10 years of recession, is still the highest in the world at $39,000, higher than even America's. For Japan's GDP to have surpassed America's in the early 1990's, Japan's per-capita GDP would have had to have been about $45,000+, which is too much to ask for. Where did you get your GDP data? The CIA WORLD FACTOBOOK and OTHER SOURCES document per capita GDP of the US is $36,200 (#2 behind Luxembourg's $36,400) while Japan's is in 14th place at $24,900.
The CIA World Factbook uses per-capita GDP figures adjusted for purchasing-power parity. I used the raw, non-adjusted per-capita GDP figures.