The burden of proof is on people stating that an AI has a theory of mind, not on the reverse. Until recently it was highly debated on if dogs have theory of mind, and it took decades of evidence to come to the conclusion that yes, they do.

GGP didn't say that AI has a theory of mind. GGP said that using AI productively requires a theory of mind, a.k.a. being able to build a mental model of the LLM's context.

The burden of proof is on the person making the claim. It doesn't matter whether the claim is positive or negative. The default position is "We don't know if AI has a ToM."

Am I incorrect in thinking this is as much true of the linux kernel or emacs as it is of an LLM?

If you read carefully you will see that they never said AI has a theory of mind.