https://doc.rust-lang.org/beta/src/std/io/stdio.rs.html#674-...
The implementation calls indeed a panicking API, OnceLock::get_or_init:
https://doc.rust-lang.org/beta/std/sync/struct.OnceLock.html...
But it only panicks if it is being used in a wrong way, which it isn't. The usage is contained within the implementation of std::io::stdout, so it's an implementation detail.
It's a shame that there are no better ways to eliminate panics in case they are impossible to trigger. The article shows some tricks, but I think the language is missing still some expressability around this, and the stdlib should also thrive harder to actually get rid of hard-to-optimize links to panic runtime in case of APIs that don't actually panic.