I think 'understand govt' is in the details of how it works. Government, at the bureaucracy level, is a large collection of paid workers. These groups of workers don't talk to each other, many don't give a damn so long as they don't get fired and most don't even understand their own rules and policies.
Each group has different procedures to accomplish a task and many of those procedures seem bizarre and obtuse when you try and navigate them to accomplish the task you are trying to actually do.
There is a huge difference between understanding the high level of how your government works and navigating the quagmire many of the departments have become.
Although from a government that seriously thought they could sell off all the forests without anyone getting annoyed, I am unwilling to assume anything.
(@alphagov turned round an answer to my question in less than a minute!)
My guess, and obviously I could be wrong, is that it was an internal joke, but not meant to be for public consumption for fear that people wouldn't get it and would criticise them for it.
In the photo, on one of those mission-statement postit notes, next to "no need to understant govt" and "task focus" there's one that says "spin is trust."
This rather sours the milk for me.