(a) if Otto is now thinking that water is wet, then he knows that he's thinking that water is wet
vs.
    (b) if Otto is now thinking that water is wet, then he knows that he's thinking that water is wet, rather than that twater is wet.

As I said in my original email, Otto doesn't need to have the thought water, rather than twater, is wet or anything like that.  But the skeptical problem that has been raised is that Otto can’t tell if he’s having WATER-thoughts or whether he’s having TWATER-thoughts.  (Whether or not Otto himself is aware of this problem is not relevant.)  So to respond to the problem, we need to see why Otto's thoughts are about water, rather than about twater. And the DBH line tries to say why Otto's thoughts are about water, (rather than about twater).  And this is because he just has a second order thought about water (and not about twater).  None of that says that he has to have a thought along the lines of that mentioned in (b) above.  As Dorit says, “Otto is not even in a position to entertain the possibility that he may be thinking that twater rather than water is wet - he simply doesn't even have the concept TWATER.”
    But this doesn’t serve to avoid the problem that Boghossian has raised for the externalist. When Dorit or Otto go through the a priori Twin Earth reasoning they
“recognize that the truth of externalism entails that certain environmental conditions must obtain for [them] to have WATER-thoughts” (to quote Dorit again). But this is where I see Dorit falling into Boghossian’s trap.  What do Dorit (and Otto) come to know?  They come to know that there must be water in their environment – and they come to know this through a priori reasoning.
    Dorit says:

“I can then go on to affirm that I am having a WATER-thought.  But I know, if I accept the DBH line, that this doesn't mean I can tell ("apriori", in virtue of knowing what I'm thinking) whether I am on earth or twin-earth.”