We can extend this analogy. What if someone put up a proxy, that has a legal Netflix subscription and which "watches" streams of Netflix shows, captures actual RGB values of pixels and re-streams the resulting video to anyone else? Isn't it the same "proxy" excuse?

I would say no because the site was happy to serve the content publicly, whereas your proxy is breaking a contractual agreement. Now we get into terms of service of a website, and even if you visit for free you agree to them. Which is a possible point. It is quite grey IMO. In terms of HN I reckon a mag would love the free brand rec. vs. the archive not being shared. Where it hurts them is if someone is avoiding paying for a subscription by continually using archive sites.

Indeed there are media that are hard paywalled, e.g., the information. However these are prohibited on HN, which possibly create additional bias towards non-hard-paywalled publications