Similar to Alex, I've got respect for the NBTHK shinsa team - but questioning doesn't equate to criticism, as Jacques seems to assert.
Any process involving people is fallible - and appealing to authority isn't enough for me. Just look at the number of misdiagnosis from medical doctors - and then the education and qualifications required to perform in those roles.
I don't know what credentials / qualifications are required to appraise a sword and signature as genuine - but I'd imagine it crosses into quite a few fields; sword and political history, forging / smithing, Japanese language knowledge (including old / archaic writing), signature analysis, materials analysis (corrosion, aging, composition etc.) and so on.
I work with a few PhDs, and whilst they're clever guys, their field of expertise narrows as the depth of their knowledge increases. They certainly don't know everything and make mistakes like anyone else. It'd be the height of hubris to assume there's nothing they could learn from less qualified or experienced people.
So, yeah, I'd view the NBTHK as a highly respected authority, and I'd want a fairly high body of evidence to challenge their opinion. That's still not criticism though - as their appraisal should hold up to scrutiny - and, as in any scientific process, be prepared to change if evidence is later presented that might suggest otherwise.