You need to apply Wittgenstein here.
This appears to be true because you haven't defined "better". If you define it, it'll become obvious that this is either false or true, but if it is true it'll be obvious in a way that doesn't make it sound interesting anymore.
(For one thing our current "AI" don't come from "writing code", they just come from training bigger models on the same data. For another, making changes to code doesn't make it exponentially better, and instead breaks it if you're not careful.)
> I guess people working there believe in magic.
Yes, OpenAI was literally founded by a computer worshipping religious cult.
> People believe that self-improvement might happen when AI is around human-level.
Humans don't have a "recursive self-improvement" ability.
Also not obvious that an AI that was both "aligned" and "capable of recursive self-improvement" would choose to do it; if you're an AI and you're making a new improved AI, how do you know it's aligned? It sounds unsafe.