I think in this scenario it seems fair to post a question. What's the alternative, write a blog article asking the same and post a link to that instead?

I'm also interested in a status update given some recent news posted on HN about Finland experimenting with the same ideas.

Alternative would be emailing them "Are you able to share any progress on the BI project? I'd bet more on HN would be keen to hear too." Project then writes a blog and someone submits to HN.

However, I can appreciate that the slight public pressure of an Ask YC making the front page might encourage quicker movement or at least a response that didn't otherwise warrant a blog post.

Agreed. This seems like the right way to ask for updates. Especially since other people would like to know too.

If YC is going to use HN to promote themselves, seems only fair to allow the community to query them via HN.

There needs to be an "Ask YC" weekly.

It'd also make for a great way to nudge the community in the desired direction by focusing attention (and away from becoming what's effectively a standalone subreddit).

Except for the fact that YC explicitly said don't do this...

Which is not necessarily a reason not too. That's the double-edge of company backed fora.

Not exactly this...

Does this count? It's just a query about updates on something YC posted on HN themselves. Seems allowed to me.

This doesn't seem in the spirit of this rule, which seems designed to prevent questions of the type 'How do I get into YC?'

Correct me if I am wrong, but user "sama" is Sam Altman, President of YC; so if he answers instead of killing the thread, I would guess he is OK with it.

Are you actually a mod though? Rule call-outs are almost always even more noisy than the original offense was.