I mean, many companies operate within particular domains but don't have much skin in the domain itself in a way that is meaningful to other participants there -- like Oracle builds software for healthcare, ostensibly, but any actual user of their products will tell you they are nightmarish with regard to usability, and research shows that patients are often harmed as a result. So healthcare isn't their game, it's selling healthcare software.

Likewise OpenAI doesn't have "skin" of any shape or value in e.g. the mathematics community or even in mathematics research per se. In my cynical view, they are exploiting the exposure of mathematical research to automation in an effort to create a case study of their product obsoleting a highly visible and well-leveraged and relatively small profession. Regardless, I doubt even they would say they have durable skin in mathematics in any sense, certainly not in either of the senses I mentioned above. But their output inhabits the same space as mathematicians, who have to contend with the consequences

OpenAI most certainly have a "skin" in math and physics.

They hire math and physics grads and good command of math is very useful in computer science, machine learning and AI.