LOL! No... not even close. Wow... I don't know who told you that one.
The Officers themselves are the blue line. They are not on a side of the line, they are the line. The blue line represents the Officers that separate chaos and order. A line that stands between the criminals and the would be victims.
You said "The basic message of the “thin blue line” is that cops will cover for each other when they break the law." You are way off, it is nothing close to that. Thanks for the good laugh though.
That was always my understanding.