I don't know, and I suspect that the task of tracking down definitively and conclusively exactly what the conditions are when I can and cannot read things would be lengthy and relatively unrewarding.
I have better things to do than play "hunt the foible" on Google.
In my experience, the conditions are pretty much as described.
If Google knows you have an account because of tracking devices, they require you to log in because you are more salable.
If you're anonymous, you're more salable if they just show you the content.
In so far as I recall, originally G+ wouldn't show content without javascript turned on - i.e. the price of content was to allow Google to track you more closely.
Nope, not without logging in. Probably need to clear cookies or something. But in any case, the grandparents are not lying or stupid afaict so stop downvoting them.
You are wrong. If you have previously logged into a Google+ account, but are not logged in, you are blocked from seeing the article w/o logging in.
To circumvent, you can put your browser into Private or Incognito browsing, and you can then read the post w/o logging in. (Which also logs you out of HN, so you can't comment or vote.)
So, for any of the HN audience with G+ accounts but who don't surf "logged in", a login is required unless the user takes extra steps (EDIT: such as incognito or child comment's noscript approach).
I have a G+ account. I don't surf "logged in." A login is not required for me to view the content. I suspect this is because surfing "not logged in" is not the starting point for improving my surfing experiences. The starting point is noscript.
Actually, there are situations in which you get a G+ login prompt. An incognito window solves it, but it's annoying. Google Groups does the same thing.
You do NOT have to login into Google+ to read the post.