With a generous interpretation, they can be said to break classical thermodynamics, since they quantum physics onto the table, most notably magnets can have negative temperature according to the statistical definition. Nothing that breaks physics at large, but would probably cause Ludwig Boltzmann a mild headache if he heard about it.
It's still not going to allow you to make perpetual motion machines, though.
Why would you use a classical model to describe a quantum system? That's the kind of wordplay that those articles do, and almost identical to my example about materials. It's entertaining, but meaningless.
Well in this case you absolutely can, the results just seem counter to our intuition about temperature. Negative temperature is a meaningful description of these types of systems.
I'm trying to explain how articles often conflate "intuition" with "breaking physics", and you're making your argument by conflating them. We're having different conversations.
This is just sophistry. You're omitting the crucial context of what it is in these sentences, and it is only when this is done they appear contradictory.
It's still not going to allow you to make perpetual motion machines, though.