Good God, it's like a scene in Guide For the Married Man in which the wife catches the husband with a naked woman and he just denies it until the woman gets dressed and leaves. And as for the brilliant conclusion that N.K. is trying to show it has changed, they announced this along with a statement that their promise to halt their nuclear program is dead!
Neither country would take the US' word for it without independently verification by their own intelligence agencies. In fact, they probably have better intelligence on the ground that we do.
So far as I have heard, the North Korean's have admitted to a uranium enrichment program. This does not mean that they have a bomb. However, even highly enriched U235 is not a particularly good bomb making material. Pu239 is much preferred. Also, uranium which has been only moderately enriched cannot be used to make a bomb, but it is useful in making nuclear reactors -- which North Korea needs in order to be self-sufficient in power generation.