According to David Lewis (1980), a context is a location (spatiotemporally centered world) where a sentence may be said (but need not contain any utterance nor speaker at the center etc.), and thus has countless features, and an index is an n-tuple of shiftable features of context. Moderate views have it that a sentence s is true at a context c iff s is true at c with respect to the index of that context i_c; and radical relativist views such as MacFarlane's depart from that.
With respect to this framework, one can characterize contextualist versions of moderate relativism endorsing the appearances of sentence s being true at c (wrt i_c) while false at c* (wrt i_c*); and in turn one can distinguish indexical contextualism (having it that this is true in virtue of s having a different content at c than c*) from non-indexical contextualism (having it that s has the same content at c and c* but that determines a different value wrt i_c than wrt i_c*.
Contexts in this sense are very rich. In particular, there is nothing as the epistemic situation (or standard or whathaveyou) of the context. There is that of the speaker at the center of the context (if one), that of the attributee of the utterance at the center of the context (if one), that which is salient in the conversation that takes place near the center of the context (if one), and so on and so forth. As Dan Z points out, this richness of contexts tends to be neglected in some discussions about knowledge attributions, and more sophisticated versions of indexical contextualism would presumably exploit this. (He still thinks that the view suffers from other “quite serious” difficulties so that it is “likely” that it will fail. I’m not convinced, but let’s discuss that in some other occasion.)
As I understand his own positive proposal, he claims that the attributions have the same semantic value across context, but are evaluated differently with respect to different indices of these context—where the epistemic standard of the context that figures as a coordinate in the index need not be that of the subject at the center of the context, nor the attributee, but is the highest (I guess among those that are relevant in the conversation that takes place near the center). But thus his seems to me to be a version of non-indexical contextualism and not radical relativism proper!