Note: I'm no expert.
A Shinsa committee is a group of people. They can be wrong. And they have considerable reason to err on the side of "no"; when they say something is shoshin they're putting their reputation and that of the organization behind that. If there's any question, they pass - and that may not mean it's gimei, it may mean simply they can't say it's shoshin (right?). Back when I was more directly involved (I worked the submission desk at the '97 Long Island NTHK Shinsa with Yoshikawa-sensei), my understanding at the time that NTHK was both more forthcoming with details (pass and fail), and also they were putting their personal guarantee on the result. I had several items pass with good results there, and a couple come back as gimei, but with details about what they actually were (one just as 'shinshinto' (gimei higashiyama ju yoshihira, absolutely no surprise), one as a specific mino school in early edo, one as unknown smith and (I forget the term - mass-produced war item, for a yoridoshi with a notare hamon).
Another possibility is that it was a mumei blade by another smith in the school, and was made gimei to the bigger name. Perhaps even the same name - mumei by a later (lesser) generation. IIRC there was a story from back then about a sword being submitted and failing as gimei; the mei being removed and it passing as the original smith. Which could be the committee screwing up -- or it could have been mumei, and someone put the right name on it (similar to the first scenario).
Imho, if you're confident, I'd consider resubmitting.
The lack of feedback from NBTHK is to me pretty ... annoying. Not even on a shoshin saying what generation it is often (though they may give a era). Clearly if they're saying shoshin and given a smith's name they know which smith/generation they're referring to; why not put it in the papers? (If I'm wrong about this, great - as I said, I'm no expert, and my direct experience was with the (original) NTHK).