This was a pretty confused argument -- though of course this is much clearer in retrospect, with the advantage of years of engagement with SSI. The problem is that contextualism is a thesis about the word 'knows', not about knowledge, while 'knowledge is the norm of assertion' seems like it must be a thesis about knowledge, not about English. In fact, something like a knowledge norm for assertion, combined with the observation that what you're allowed to assert depends on your situation, provides a pretty good argument for SSI; I take it to be exactly parallel to the main argument for SSI that Stanley and Fantl and McGrath give.
In chapter 3 of his new book The Case for Contextualism, DeRose essentially reproduces the content of that 2002 paper, but he does add about two new pages of material designed to correct this aspect of the original. Now, in contrast to earlier, he recognizes the need to clarify the statement of the knowledge norm of assertion, if it is to be understood in contextualist terms. He gives us:
The Relativized Knowledge Account of Assertion (KAA-R): A speaker, S, is well-enough positioned with respect to p to be able to properly assert that p if and only if S knows that p according to the standards for knowledge that are in place as S makes her assertion. (99)
Just to flag a broader source of uneasiness than is my focus in this post, I'm not really clear just what 'standards' are in this context, and I'm surprised by the invocation of 'knows that p according to such-and-such standards', which I guess is meant to be invariantist. But I'm taking the right-hand side of KAA-R to be equivalent to: 'S knows p' expresses a truth relative to the context in which S is participating. The central feature of KAA-R is that it's the subject's context that is relevant for whether the KAA-R condition is met; we're not being contextualists about 'well-enough positioned' or anything like that. DeRose contrasts KAA-R with KAA-R2:
KAA-R2: A subject, S1, is well-enough positioned with respect to p to make true the claim of a speaker, S2, that S1 is ' warranted in asserting that p' if and only if S1 knows that p according to the standards for knowledge that are in place in S2's context as S2 makes her claim. (99)
KAA-R2 is presented rather confusingly, I think. As far as I can tell, it's equivalent to this much more easily-digestable thesis: In all contexts, "S is well-enough positioned with respect to p to assert that p iff S knows that p" is true. But anyway, that's a side note. DeRose doesn't say why he prefers KAA-R over rivals like KAA-R2 (unless he does so later than the point I've read up to), but only mentions KAA-R2 to illustrate that KAA-R is his preferred gloss on the knowledge norm of assertion.
I have some concerns about KAA-R as a statement of the knowledge norm for a contextualist. Here are two; one I'm more confident about, and one I'm more tentative about.
(1) Given contextualism about 'knows', KAA-R is consistent with the truth of many sentences of the form "S doesn't know that p but it's entirely appropriate for her to assert that p." KAA-R predicts the truth of such sentences any time the attributor is in a skeptical context and S is in a nonskeptical one. But if you accept the knowledge norm of assertion, you should not think that sentences like that are ever true. Therefore, KAA-R does not capture the knowledge norm of assertion. A similar problem befalls sentences like "S knows that p, but she is not in a strong enough epistemic position to assert that p." KAA-R2 enjoys a clear advantage here.
(2) KAA-R cites the "standards for knowledge that are in place as S makes her assertion". I worry whether there will be a unique such set of standards -- it seems like there might not be, especially since S's assertion is just the assertion that p; S isn't attributing or denying knowledge. If part of what sets the relevant standards is a kind of scoreboard/accommodating process, then the act of attributing or denying knowledge plays a key role in fixing the relevant standards. Maybe DeRose just thinks this can never happen; I guess we need to know more about what it is in virtue of which the operative standards in a given context are what they are. KAA-R is in trouble, I think, if there are possible situations where one could say "S knows p" or one could say "S doesn't know p", and either would express a truth, because the context would shift to accommodate it. I'm inclined to think there are cases like this. If that's right, then there might not be any operative 'standards for knowledge' in S's context.