That phrase is used exactly to say that there is a third unseen force influencing both events. It’d be pretty strange to use that phrase to say the opposite.
Typically further discussion of the 3rd event isn’t relevant, because they’re not trying to find the cause, they’re trying to disprove a hypothesis.
I’ve seen it used to end discussions. People repeat the wisdom of the phrase without understanding what you just said.
There could just be no connection at all. Like how there’s a positive correlation between shark attacks and box office sales for Nick Cage movies. There might be some relation between them, but more likely there is no link and it’s just random noise that happens to line up particularly well.
The reason why you might see it used as an end statement is because there is no data or clear logical link between the subjects which were correlated. It’s basically saying “unless you have some reason to believe they’re linked, you should probably assume they’re not”
