Based on my interactions with Patrick it seems to be genuine. When I interned at Stripe he randomly sat down with me at lunch and we talked about taxes for half an hour.
I think the founder and CEO of a large, valuable company randomly sitting down with an intern to discuss some topic for 30 minutes illuminates something about their personality, even if that alone isn't proof they're a saint or anything.
It's the collection of anecdotes like that, the absence of counter-anecdotes, and little things like Patrick still sometimes commenting on HN that paint a fuller picture. Such a person could still potentially be hiding a darker side, but I think it decreases the probability.
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".
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.