Clarifying global custom linked variables -unlocked

I find conflicting details of global custom variables. I built a global custom variable with a Linked Value and Unlocked. Some documentation, and the popup description make me believe that a flow using global_var_set will update the variable value and this value will persist across engagements so long as the value is set to unlocked. But another document has a "Note:" that contradicts this. 

The behavior I am seeing is that the global var is not persistent and any new engagement receives the default value set in the Preference-Variables section.

I need the opposite behavior. I need a variable to be updated in a flow of one engagement and that latest value to be persistent and sent to all following flows. Am I setting a parameter incorrectly or missing an argument in a script possibly?