Maybe NH gave UA/MP incorrect information re: your flight? Have you contacted MP? What did they say? I'd write/fax a letter with boarding pass to MP in the U.S.A. and/or call the MP service center in the U.S.A. I'd check with NH also just to make sure they credit 5,960 for this flight for their own fliers.
I seem to recall that NH used to credit some low-priced economy fares at 70% so if this is still the practice it might explain your credit?
http://www.united.com/page/article/0,,1182,00.html
Earning miles
All Nippon Airways (ANA) is one of 14 globe-spanning members of the Star Alliance network. Our partnership with All Nippon Airways extends your Mileage PlusŪ benefits to destinations across Japan. Simply present your Mileage Plus number when you make your reservations and you can earn:
International flights:
50% of actual miles flown in inclusive tour discount-fare Economy Class
70% of actual miles flown in published discount-fare Economy Class
100% of actual miles flown in full-fare Economy Class
125% of actual miles flown in Business Class
150% of actual miles flown in First Class