Thats correct!
The guy sees two black hats. It means his hat is either black or white.(There are only two choices so .. yea)
If his hat is white,
it means his opponents would have seen this:
ONE BLACK HAT, ONE WHITE HAT.
ASSUMING that his WISE opponents are actually WISE (though i doubt this is something we would want to argue about)
...they would know very clearly that if their hats are white,
then there would be TWO WHITE HATS and the last remaining person with the Black Hat will IMMEDIATELY know that his hat is black.
However, this person with the black hat had not IMMEDIATELY realised his hat was black. And why was that? That was because he DID NOT SEE TWO white hats! Which means what he saw, was A BLACK and a WHITE Hat. Since the one who is wearing the WHITE HAT is the first wise guy, it means their own hat is black.
Therefore, his opponents would have guessed after a very SHORT while that their own hat is BLACK.
However, that was not the case. ALL of them were confused and nobody knew what to do? The only reason is that, there were THREE BLACK HATS.
Great job!