I'm assuming you have this variable linked to a Check Box? In that case I think what you are seeing is a bit of a Red Herring. I have created a 'Set Variable' Action using 'Yes' and 'No' and although the note changes to 'Text' (as you noted), the Check Box updates fine. I also used Dispatch to turn the 'checkbox' on and off using 1 and 0 as the values... again all updated on the card fine.
I am not using against a checkbox, rather just as a flag for a do-while loop.
I get the same results with the variable type being listed as "text" in the Action tab but it all seems to function fine.
Not sure why it didn't work at first - but now all is well.
I will just have to scratch my head and move on at this point.