First, IANAL, so my use of some terms may be loose. I never intend to convey more than an informed layman's opinion. However, I do love it when I'm corrected so that my usage can improve.
Fair use is an affirmative defense. Google admits that it copies content without legal license to do so, but claims that said copies are non-infringing under fair use exemptions. I guess you're probably correct that it's no longer appropriate to refer to Google's behavior specifically as "infringing", just "copying without authorization", which, for those of us without $5 million to commit to a legal team, means "infringing". I will try to remember the special standard of law which has been allowed to Google and refer to their copying only as "unauthorized" and not "infringing" in the future.
If you review the points summarized in the Wikipedia articles you helpfully linked, you'll see that Google's defense is mostly "Yeah, but we're Google".
In Field, "the court found that the plaintiff had granted Google an implied, nonexclusive license to display the work because of Field’s failure in using meta tags to prevent his site from being cached by Google.", i.e., because Field already knew Google existed and knew there was a standard way to prevent its access but chose not to employ it, he gave Google an implied license.
Who else does that work for? Can I send an email to Netflix and tell them "Hey, if you don't want me to copy your shows, please add this in your page's HEAD element: "? No?
I understand there are other criteria which were used to decide if Google's use was specifically infringing in addition to the implied license. Just demonstrating that Google is getting favored treatment from the judiciary that would not be available to a normal entity.
In Perfect 10 [0], the judge even explicitly indicated that he was loathe to find Google's use of thumbnails infringing because he didn't want to "impede the advance of internet technology", but that he felt the law obligated him to do so (his ruling in that matter was overturned on appeal, when the Ninth Circuit found Google's usage non-infringing). What if the defendant had been some company perceived as less technically advanced than Google? This is probably as close as you can get to an explicit statement of favoritism. The Ninth Circuit also rejected Perfect 10's claim that RAM copies were infringing (which was not the case with an unlucky non-Google company discussed further down).
What if I started indexing and rehosting thumbnails? I can assure you that I would get C&D'd almost immediately and I would be forced to shut down because I can't afford to pay lawyers for 3 years while the case works through the system (and to be honest, I'm surprised it only took 3 years). And even if I could, with a reputation less sterling than Google's, there's no reason to believe that a judge would rule in the favor of one useless guy instead of a big company. A judge would look at the case and say "Google's use was fair because it provided a public service [actually cited as part of the justification in most of your linked cases], but this guy is just using it for a few hundred people, it's definitely unfair, he owes that company more money than he'll make in his life, case dismissed".
There are many such cases on the books. I don't know if Google has a direct connection to the reptilian overlords or what, but it seems in most cases where they're not involved, the good side loses.
In Craigslist v. 3Taps, while primarily a CFAA case, 3Taps was found to be infringing copyrights by sampling Craigslist postings in order to allow its clients to plot them on a map. Being a "public service" or a "referential use" didn't matter for them. They were raked over the coals, and it's been that way with most cases.
In Ticketmaster v. RMG Technologies [1], RMG was found to infringe just by parsing a page. "Defendant's direct liability for copyright infringement is based on the automatically-created copies of ticketmaster.com webpages that are stored on Defendant's computer each time Defendant accesses ticketmaster.com. [...] Defendant contends [...] that such copies could not give rise to copyright liability because their creation constitutes fair use[.] [...] Defendant's fair use defense fails."
The case specifically discusses how, despite the precedent in Perfect 10, since the Defendant is not Google, it is bound by a site's Terms of Use and copyright law, and RAM copies, which are specifically non-infringing for Google, were infringing for RMG.
Very similar findings were made in Facebook v. Power Ventures, and the founder was left holding a bag of $3 million in personal liability.
This is a thread about the legality of HN users scraping. It seems Google is the only entity capable of making unauthorized copies and then getting courts to agree that it's fair use. For the rest of us, it's infringement, which carries stiff penalties (and this doesn't even broach the CFAA portion of the issue).
So when I say "infringing", I mean something that would be considered infringing if you aren't Google. It's apparently only infringement if the judges involved don't personally use your site and don't have to worry about personally suffering the consequences of not having access to it. :)
[0] https://www.eff.org/document/perfect-10-v-google-ninth-circu...
[1] https://scholar.google.com/scholar_case?case=147697505884223...