[nl]

This isn't correct.

People who care about status see "intern" as a low-status label, and well below their "CEO" high-status label.

The fact that he spent time with an intern indicates that he doesn't care particularly about the status of these labels. In many cases this is called "being nice".

[akhilcacharya]

I really don't think they see intern as a low status label, especially if they have an MIT jacket on, for example.

I worked at a company with a CEO that did something similar and asked interns to come to his desk to chat, which I did. This practice didn't exactly shield him from being cast as an out of touch billionaire when he ran for President.