Kvanvig conflates sensitivity to context with non-rigidity, but a term can be context-sensitive yet rigid once context is fixed, as 'I' demonstrates in Kaplan's logic of indexicals.
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In philosophy of language, a term is rigid if it always refers to the same thing no matter what situation you're imagining; it doesn't change its meaning across different scenarios.
context-sensitive(Used to describe terms like 'I' and 'left' whose reference shifts with the context of use.)
A term whose semantic value or referent varies depending on features of the context of utterance, such as the identity or orientation of the speaker.
indexicals(Philosophy of language, semantics)
Expressions whose reference depends on the context of utterance, such as 'I' or 'here'