I discovered "Invalid JSON string" had no hits in the docs but scores on the forums and tracker.
O added an FAQ as a bit of a laceholder in case someone can write something both clear and authoritative: http://docs.moodle.org/22/en/File_picker_FAQ#How_can_I_solve_the_.22Invalid_JSON_string.22_error.3F
It did get me curious, that I knew very little about why this error keeps re-surfacing, now on several versions of Moodle 2+ and several servers.
Two random forum discussions that show the comlexity of the issue:
It seems the error is a very general one and can cover up a lot of difference causes. Anyone is welcome to add to the FAQ