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)