[hakuseki]

Actually this is an example of ambiguity, not context sensitivity (in the formal languages sense). Context sensitivity means context is needed to construct a grammatical sentence, not merely to parse one. It's actually pretty hard to find examples of this in natural language.

[thaumasiotes]

Judging by the paper linked sidethread, it's enough that some valid sentences cannot be constructed in a context-free way. Even if they can be losslessly transformed into alternative sentences which can be easily derived from a context-free grammar, their existence demonstrates that the language is not context-free.