There's a lot going on with this phrase. The message being conveyed is that if something is getting the job done, then it can be left alone.
I've usually heard this phrase used when talking about a job that is complex, expensive, or tedious. Especially when getting something in perfect working order will not substantially improve the function. A car door with a dent in it might cost $1500 to fix, but it still locks and opens easily.
There's also a lot of meaning in the word 'broke'. Broke implies that something is unable to fulfill it's function. In our car door example, the door is damaged but still able to perform its function. I see this phrase used to drive home the point that damaged does not always need to be fixed.
Finally, take the phrase you're asking about. It's incorrect on a number of levels but because it is adequately conveying it's message it does not need to be fixed.