The user of the phrase is conceding that the argument isn’t the point. The aspirational head-tenant has dropped the pretense of argument altogether, freeing themselves to simply point out that the involved parties hate each other, and hate takes headspace. In that sense, sure, it is the “perfect” insult of our times. But it almost makes you wish for the quainter days of internet abuse.
As a remark, “rent-free” is totally devoid of content, not even reaching the level of a burn or own. Which is telling: the standard of discourse has sunk below the level of bare fact, below reckless opinion, below even a nice spicy ad hominem. Those would all require too much creative juice or fine-tuning. At this point, merely gesturing at the fact that you have been having the conversation at all qualifies as a trump card for certain people, e.g. terminally red doofuses pulsing with the dammed-up sensation of not having eaten a vegetable in eight months. It is for people who do not want to provoke you with any particular fact so much as they want you to notice that they have been provoking you for a while. Just empty provocations all the way down.