To the examples, fly.io caught my attention primarily by offering a useful free tier DB, and tailscale has my attention as a "beat this" offering for some homelab access stuff (meaning some stuff could but I at least have a benchmark). Until this post I didn't actually know one was YC and another wasn't. I'm interested in both purely because of HN posts.
I put the OP in the second-chance pool (https://news.ycombinator.com/pool, explained at https://news.ycombinator.com/item?id=26998308), but that was according to the usual 5-second standard of "I think the community might like this one". I didn't look closely enough to tell whether the article was positive or negative towards Fly.io, nor is it our job to care about that. What we care about is intellectual curiosity (see https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...).
There's one big exception to the above, which is the official Launch HN posts we do for YC startups - those are described at https://news.ycombinator.com/newsfaq.html - they get official placement on HN's front page, as explained there. But they're always clearly indicated by "Launch HN".
I personally find it super interesting which startups end up achieving HN darling status - the classic examples of this are Stripe and Cloudflare - I'd add Hashicorp - and it would be fun to make a list of others. But from a moderation point of view it doesn't matter whether such a startup is YC-funded or not and we try to be as neutral as we can that way. I'm not saying we don't have unconscious biases or conflicts of interest (such a claim is impossible!) but we're strict about how we approach this consciously, and we have quite a lot of practice with that.
It's a natural concern of course, and I'm always happy to answer questions.
p.s. Incidentally, there's at least one HN user who has made a long series of accounts angrily accusing us of secretly favoring a non-YC startup (the one mentioned in the GP comment). We haven't, but because that startup is well-loved by the community, it's easy to see how it could come across that way, with threads appearing frequently and filling up quickly with comments.